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   With the help of GEMM it should be possible to supplement present QA
   mechanisms, by adding a component that automatically locates and list
   bugs of a new nature.

   This can be compared and contrasted against a test suite which is slow
   to incorporate new material, and as a result is rather static in nature.

   GEMM, on the other hand, is dynamical and continually searching various
   branches of behavior.

   It is anticipated that on a time scale of 12 months, that GEMM should be
   able to locate examples of new bugs for hundreds system functions, many
   thousands classified nice-formatted entries like the samples shown below.

   Please completely realize that:

            * the structure of an entry is under  y o u r  control
            * the choice of the function is under  y o u r  control

   Had you have any questions please don't hesitate to contact me at
   vvb@mail.strace.net.  Enjoy!


   Sincerely,
   VB


...............................................................................

                        TESTING ENVIRONMENT

CPU ID          AuthenticAMD AMD Athlon(tm) XP 1600+
RAM size        512 Mb
Free HDD size   11  Gb
OS ID           Microsoft Windows 98 4.10.2222 A

...............................................................................

                        MEANINGS OF THE MARKERS

ABSENT          The result of the evaluation is correct
BUG-1           The bug differs from the bug in Maple 8
CANNOT          The expression is returned unevaluated
CRASHED         Invalid memory addressing occurred
ERROR           An error message interrupted the computation
LOOPED          The expression is running after 2 hours
PRESENT         The quoted bug is present in the output
REGRESSION      At least 1 Maple version can handle it correctly
REPRODUCIBLE    The bug can can be reproduced
UNDONE          Maple transformed the input without full success

...............................................................................
BUG # 1 (software protection)

****************************************
***  UNRELIABLE SOFTWARE PROTECTION  ***
****************************************

ACTUAL:         Can make Maple 8 Trial Version copy running forever.

HOW-TO-DO:      Keep/reset the system date within 29 days after
                the date of the installation.

EXPECTED:       Cannot run Maple 8 Trial Version after 30 days.

FORMAL ADVICE:  1) Consider SciFace experience.
                2) Consider WRI experience.
                3) Consider TI experience.
                4) Consider the ideas of Vladimir V. Bondarenko.
                5) Consider using dongles.

TRUE ADVICE:    Keep her steady! ;-)

...............................................................................
BUG # 2 (evalf)

**************************************
***  INVALID PAGE FAULT EXCEPTION  ***
**************************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(AiryAi(1/sqrt(z)), z=0..1));

ACTUAL:         MSERVER caused an invalid page fault in module MAPLE.DLL
                at 0167:1016d5af.

EXPECTED:       .07316096643

...............................................................................
BUG # 3 (evalf)

**************************************
***  INVALID PAGE FAULT EXCEPTION  ***
**************************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ERROR 4    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ERROR 3    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR 2    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR 1    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(StruveH(1/3,1/z), z=0..1));

ACTUAL:         MSERVER caused an invalid page fault in module MAPLE.DLL
                at 0167:1016d5af.

EXPECTED:       .5386098780

The same problem with

                evalf(Int(StruveH(1/3,1/sqrt(z)), z=0..1));

...............................................................................
BUG # 4 (evalf)

**********************************
***  MEMORY ALLOCATION FAILED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ABSENT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                LOOPED     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(arccosh(1/tanh(z)), z=-1..1));

ACTUAL:         Execution stopped: Memory allocation failed.
                The kernel has been shut down.
                Further computations cannot be performed.

EXPECTED:       3.439997633+3.141592654*I

CHECK-UP:       evalf(Int(arccosh(1/tanh(z)), z=-1..0))+
                evalf(Int(arccosh(1/tanh(z)), z=0..1));

                3.439997634+3.141592654*I

The same problem with

                evalf(Int(arccosh(1/tanh(z)), z=-1..0))+
                evalf(Int(arccosh(1/tanh(z)), z=0..1));

...............................................................................
BUG # 5 (int)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(exp(z)*ln(z), z=infinity..0);

ACTUAL:         Error, (in limit) inconsistent direction with infinities

EXPECTED:       -infinity

CHECK-UP:       evalf(Int(exp(z)*ln(z), z=infinity..0));

                Float(-infinity)

                evalf(Int(exp(z)*ln(z), z=100..0));

                -.1235208139e45

...............................................................................
BUG # 6 (int)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(arctan(sqrt(3)*(2*z - 1)/3)/(z^2 + 1), z=0..infinity);

ACTUAL:         Error, (in signum/main) numeric exception: division by zero

EXPECTED:       13/288*Pi^2+1/16*ln(7-4*3^(1/2))*ln(2-3^(1/2))+1/4*dilog(-2/(-\
                2-I+3^(1/2)))+1/4*dilog(-2/(-2+I+3^(1/2)))+1/4*dilog((3*I+3^(1\
                /2))/(3*I+(1+2*I)*3^(1/2)))+1/4*dilog((3+I*3^(1/2))/(3+(2+I)*3\
                ^(1/2)))

CHECK-UP:       .8224670361+0.*I

                evalf(Int(arctan(sqrt(3)*(2*z-1)/3)/(z^2+1), z=0..infinity));

                .8224670334

...............................................................................
BUG # 7 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                CANNOT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                LOOPED     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CRASHED    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                LOOPED     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                a := 1/10^10:

                evalf(Int(Int(Int(1/(3 - cos(x) - cos(y) - cos(z)), x=a..Pi-a),
                y=a..Pi-a), z=a..Pi-a));

ACTUAL 1 (often):   Error, (in property/OrProp/*) too many levels of recursion

ACTUAL 2 (seldom):  Error, (in collect/series) too many levels of recursion

...............................................................................
BUG # 8 (evalf)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ERROR 2    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR 2    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR 1    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(arcsec(1/arccsch(z)), z=-1..1));

ACTUAL:         Error, (in evalf/int) cannot assume on a constant object

EXPECTED:       3.141592654

CHECK-UP:       evalf(Int(arcsec(1/arccsch(z)), z=-1..0))+
                evalf(Int(arcsec(1/arccsch(z)), z=0..1));

                3.141592654+0.*I

The same problem with

                evalf(Int(arcsec(1/arccsch(z)), z=-0.99..0.99));
                evalf(Int(arccsc(1/arccsch(z)), z=-1..1));

...............................................................................
BUG # 9 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                UNDONE     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                UNDONE     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(I^z, z=0..infinity);

ACTUAL:         Error, (in limit/range) invalid terms in sum

EXPECTED:       undefined

...............................................................................
BUG # 10 (int)

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 1      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                BUG 1      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(arctan((z - 1))/(z^2 + 1), z=0..infinity),30);

ACTUAL:         .328636331315204260235482460675-.8e-30*I

EXPECTED:       1/8*ln(-1/5+2/5*I)^2+1/6*Pi^2+1/8*ln(-1/5-2/5*I)^2-1/8*I*ln(2-\
                I)*Pi+1/8*I*ln(2+I)*Pi + 1/16*I*Pi*ln(2)-1/8*I*ln(1-I)*Pi+1/4*\
                dilog(3/5+1/5*I)+1/4*dilog(3/5-1/5*I)

                .31465653030289119628

CHECK-UP:       evalf(Int(arctan((z - 1))/(z^2 + 1), z=0..infinity),30);

                .314656530302891196278478318862

The same problem with

                int(arctan((z + 1))/(z^2 + 1), z=0..infinity)
                int(arctan((2*z - 1)/3)/(z^2 + 1), z=0..infinity);
                int(arctan((2*z - 1))/(z^2 + 1), z=0..infinity);

...............................................................................
BUG # 11 (int)

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int((sin(1)-sin(z/(1+z)))^2, z=0..infinity);

ACTUAL:         -1+Si(2)*cos(2)-sin(2)*Ci(2)-I*sin(2)*Pi+cos(1)^2+2*sin(1)*cos\
                (1)*Ci(1)+2*I*sin(1)*cos(1)*Pi+2*Si(1)*sin(1)^2

                -.114183263+0.*I

EXPECTED:       -1/2+(Ci(1)-Ci(2)+ln(2))*sin(2)+Si(1)+1/2*cos(2)*(1-2*Si(1)+2*\
                Si(2))

                .5160936848

CHECK-UP:       evalf(Int((sin(1)-sin(z/(1+z)))^2, z=0..infinity));

                .5160936847

...............................................................................
BUG # 12 (int)

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(exp(-z^2)*arctan(z^3),z=0..infinity));

ACTUAL:         .1084191096

EXPECTED:       .2744301134

ANSWER:         See Maple V Release 5

The same problem with

                int(exp(-z^2)*arctan(z^5),z=0..infinity);
                int(exp(-z^2)*arctan(z^7),z=0..infinity);
                int(exp(-z^2)*arctan(z^9),z=0..infinity);
                int(exp(-z^2)*arctan(z^11),z=0..infinity);

...............................................................................
BUG # 13 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  MEANINGLESS OUTPUT  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The answer depends on the integration variable.

                type(int(BesselJ(1, 1/sqrt(z)), z=-1..1), freeof(z));

ACTUAL:         false

EXPECTED:       true


                int(BesselJ(1, 1/sqrt(z)), z=-1..1);

ACTUAL:         (-z^(1/2)*BesselJ(0,1)*StruveH(1,1)+z^(1/2)*BesselJ(1,1)*Struv\
                eH(0,1)-(-z)^(1/2)*BesselI(0,1)*StruveL(1,1)+(-z)^(1/2)*Bessel\
                I(1,1)*StruveL(0,1))*Pi/z^(1/2)

EXPECTED:       -2/3+4/3*BesselJ(0,1)-1/3*Pi*(BesselJ(0,1)*StruveH(1,1)-
                BesselJ(1,1)*StruveH(0,1))

CHECK-UP:       .4566187310

                evalf(Int(BesselJ(1, 1/sqrt(z)), z=0..1));

                .4566187311

...............................................................................
BUG # 14 (int)

****************************
***  MEANINGLESS OUTPUT  ***
****************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The answer involves  trunc(`limit/mrv/Re`(-1))

EXAMPLE 1:      int(sin(1/tanh(z)), z=-1..1);

ACTUAL:         1/2*I*sin(1)*Pi+1/2*I*trunc(`limit/mrv/Re`(-1))*Pi*sin(1)

EXPECTED:       0

CHECK-UP:       evalf(Int(sin(1/tanh(z)), z=-1..0))+
                evalf(Int(sin(1/tanh(z)), z=0..1));

                0


EXAMPLE 2:      int(cos(1/tanh(z)), z=-1..1);

ACTUAL:         -Si(2/(exp(-1)-exp(1))*exp(-1))*sin(1)-
                Ci(-2/(exp(-1)-exp(1))*exp(-1))*cos(1)-
                Si(2/(exp(-1)-exp(1))*exp(1))*sin(1)+
                Ci(-2/(exp(-1)-exp(1))*exp(1))*cos(1)-Pi*sin(1)-
                1/2*I*trunc(`limit/mrv/Re`(-1))*Pi*cos(1)-1/2*I*Pi*cos(1)

                -.8487048775*I*trunc(`limit/mrv/Re`(-1))-.414495363-
                .8487048775*I

EXPECTED:       -Si(2*exp(-2)/(exp(-2)-1))*sin(1)-Ci(-2*exp(-2)/(exp(-2)-1))*\
                cos(1)-Si(2/(exp(-2)-1))*sin(1)+Ci(-2/(exp(-2)-1))*cos(1)-Pi*\
                sin(1)

                -.414495363

CHECK-UP:       evalf(Int(cos(1/tanh(z)), z=-1..0))+
                evalf(Int(cos(1/tanh(z)), z=0..1));

                -.4144953636

The same problem with

                int(sqrt(sinh(z)), z = -1..1);

...............................................................................
BUG # 15 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  MEANINGLESS OUTPUT  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The answer depends on the integration variable.

                int(sqrt(z)*sqrt(1+z^2)/sqrt(1+z^6), z = -infinity..infinity):

                evalf(%);

ACTUAL:         2.831474421*(z^(1/2)+(-1.*z)^(1/2))/z^(1/2)

EXPECTED:       (1+I)*1/60*(5*GAMMA(3/4)^2*sin(5/12*Pi)*sin(1/12*Pi)* GAMMA(7/\
                12)*GAMMA(11/12)*hypergeom([1/2,5/6, 7/6, 3/4],[5/4, 4/3, 5/3]\
                ,1) - 48*GAMMA(3/4)^2*sin(5/12*Pi) * sin(1/12*Pi)*GAMMA(7/12)*\
                GAMMA(11/12)*hypergeom([1/2, 11/12, 7/12, 1/4],[17/12, 3/4, 13\
                /12],1)+5*Pi^2*hypergeom([1/2, 1/6, 5/6, 5/12],[11/12, 2/3, 4/\
                3],1)+10*Pi^2*hypergeom([1/2, 1/6, 1/12, -1/6],[2/3, 7/12, 1/3\
                ],1))/Pi^(1/2)*csc(5/12*Pi)*csc(1/12*Pi)/GAMMA(7/12)/GAMMA(11/\
                12)

CHECK-UP:       2.831474419+2.831474419*I

                evalf(Int(sqrt(z)*sqrt(1 + z^2)/sqrt(1 + z^6), z = -infinity..\
                infinity));

                2.831474417+2.831474417*I

...............................................................................
BUG # 16 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 1      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CANNOT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      int(abs(sqrt(z/(1+z^2))), z = -infinity..infinity);

ACTUAL:         undefined

EXPECTED:       infinity

CHECK-UP:       evalf(Int(abs(sqrt(z/(1+z^2))), z = -infinity..infinity));

                Float(infinity)


EXAMPLE 2:      int(abs(sqrt(z))/sqrt(1+z^2), z = -infinity..infinity);

ACTUAL:         undefined

EXPECTED:       infinity

CHECK-UP:       evalf(Int(abs(sqrt(z))/sqrt(1+z^2), z = -infinity..infinity));

                Float(infinity)

...............................................................................
BUG # 17 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

************************************
***  TRIVIAL INTEGRAL IS UNDONE  ***
************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

This integral obviously diverges because the integrand is continuous, and it
asymptotically equals to 1/sqrt(z) + O((1/z)^(5/2)) at  z = infinity, and
z^(1/2)+O(z^(5/2)) at z = 0.

I consider the Maple's 8 answer as a bug because the integral is TRIVIAL
that is can be immediately done in mind.

                int(sqrt(z/(1+z^2)), z = 0..infinity);

ACTUAL:         limit((2*(z/(1+z^2))^(1/2)*(-I*(z+I))^(1/2)*2^(1/2)*(I*(z-I))^\
                (1/2)*(I*z)^(1/2)*EllipticE((-I*(z+I))^(1/2),1/2*2^(1/2))-(z/(\
                1+z^2))^(1/2)*(-I*(z+I))^(1/2)*2^(1/2)*(I*(z-I))^(1/2)*(I*z)^(\
                1/2)*EllipticF((-I*(z+I))^(1/2),1/2*2^(1/2))+2*(z/(1+z^2))^(1/\
                2)*(-I*(z+I))^(1/2)*2^(1/2)*(I*(z - I))^(1/2)*(I*z)^(1/2)*z^2*\
                EllipticE((-I*(z+I))^(1/2),1/2*2^(1/2))-(z/(1+z^2))^(1/2)*(-I*\
                (z+I))^(1/2)*2^(1/2)*(I*(z-I))^(1/2)*(I*z)^(1/2)*z^2*EllipticF\
                ((-I*(z+I))^(1/2),1/2*2^(1/2))-2*(z*(1+z^2))^(1/2)*(z^3+z)^(1/\
                2)*EllipticE(1/2*2^(1/2))+(z*(1 + z^2))^(1/2)*(z^3 + z)^(1/2)*\
                EllipticK(1/2*2^(1/2)) -2*I*(z*(1 + z^2))^(1/2)*(z^3+z)^(1/2)*\
                EllipticE(1/2*2^(1/2)) + I*(z*(1 + z^2))^(1/2)*(z^3 +z)^(1/2)*\
                EllipticK(1/2*2^(1/2)))/(z*(1+z^2))^(1/2)/(z^3 + z)^(1/2),z = \
                infinity)

EXPECTED:       infinity

CHECK-UP:       evalf(Int(sqrt(z/(1+z^2)), z = 0..infinity));

                Float(infinity)

...............................................................................
BUG # 18 (int)

******************************
***  INVALID Im MAGNITUDE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CRASHED    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(sqrt(csc(z)), z = -1..1);

ACTUAL:         2.034805316-2.034805318*I

EXPECTED:       2.034805316+2.034805318*I

CHECK-UP:       evalf(Int(sqrt(csc(z)), z = -1..1));

                2.034805316+2.034805318*I

...............................................................................
BUG # 19 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 2      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      evalf(int(arctan(z)/(1+z^3), z=0..1),30);

ACTUAL:         .295402437233686437670241585805+.100e-29*I

EXPECTED:       .332572518837625079597240253208

CHECK-UP:       evalf(Int(arctan(z)/(1+z^3), z=0..1),30);

                .332572518837625079597240253208


EXAMPLE 2:      evalf(int(arccot(z)/(1+z^3), z=0..1),30);

ACTUAL:         1.01723170411092331267670505565-.10e-29*I

EXPECTED:       .980061622506984670749706388244

CHECK-UP:       evalf(Int(arccot(z)/(1+z^3), z=0..1),30);

                .980061622506984670749706388244

...............................................................................
BUG # 20 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CANNOT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(ln(z^2 - z + 1)/(z^2 + 1), z=0..infinity));

ACTUAL:         -2.600402544+0.*I

EXPECTED:       1/24*Pi*(-7*ln(2-3^(1/2))+13*ln(2+3^(1/2)))+
                1/2*I*(polylog(2,(I+3^(1/2))/(2+I+3^(1/2)))+
                polylog(2,1+2/(-2-I+3^(1/2)))-polylog(2,1+2/(-2+I+3^(1/2)))-
                polylog(2,1-2/(2-I+3^(1/2))))

CHECK-UP:       1.536942713+.1000000000e-9*I


                evalf(Int(ln(z^2 - z + 1)/(z^2 + 1), z=0..infinity));

                1.536942710

...............................................................................
BUG # 21 (int)

****************************
***  SPURIOUS undefined  ***
****************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ABSENT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CANNOT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

This integral must be positive.

                int(int(1/(1 + x + y)^3, x = 0..infinity), y = 0..infinity);

ACTUAL:         undefined

EXPECTED:       1/2

CHECK-UP:       evalf(Int(Int(1/(1 + x + y)^3,x=0..infinity), y=0..infinity));

                0.5000000000

...............................................................................
BUG # 22 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

***************************************************
***  INVALID Re MAGNITUDE / SPURIOUS undefined  ***
***************************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ERROR 1    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR 1    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR 2    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

This integral must be positive.

However, Maple 8 always returns one of these invalid answers:
either dilogarithms (almost always)  or  undefined (rarely).

                int(arctan(z)/(1+z^3), z=0..infinity);

ACTUAL:         dilogarithms (negative num value)  OR  undefined (wrong)

EXPECTED:       (1/144)*(4*Pi*(sqrt(3)*Pi+ln(97/8+7*sqrt(3)))-Psi(1,5/12)+\
                Psi(1,11/12))

CHECK-UP:       .7190728728

                evalf(Int(arctan(z)/(1+z^3), z=0..infinity));

                .7190728725

The same problem with

                int(arctan(z)/(1+z^4), z=0..infinity);
                int(arctan(z)/(1+z^5), z=0..infinity);

...............................................................................
BUG # 23 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ERROR 1    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ERROR 1    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                UNDONE     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

int(int(int(1/(3 - cos(x) - cos(y) - cos(z)), x=0..Pi), y=0..Pi), z= 0..Pi);

ACTUAL:         Error, (in gcd/doit) too many levels of recursion

EXPECTED:       4*Pi*(18 + 12*sqrt(2) - 10*sqrt(3) -
                7*sqrt(6))*EllipticK((2 - sqrt(3))*(sqrt(3) - sqrt(2)))^2

CHECK-UP:       15.67249482

                a := 1/10^7:

                evalf(Int(Int(Int(1/(3 - cos(x) - cos(y) - cos(z)), x=a..Pi-a),
                y=a..Pi-a), z=a..Pi-a));

                15.67247795

...............................................................................
BUG # 24 (int)

************************************************************************
*** FEATURE REQUEST: TOO COMPLICATED - CAN BE EXPRESSED MUCH SIMPLER ***
************************************************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(1/sqrt(sech(z)), z=0..infinity);

ACTUAL:         2^(1/2)*EllipticPi(1,1/2*2^(1/2))

EXPECTED:       infinity


                int(sqrt(cosh(z)), z=0..infinity);

ACTUAL:         2^(1/2)*EllipticPi(1,1/2*2^(1/2))

EXPECTED:       infinity


                int(1/sqrt(1/cosh(z)), z=0..infinity);

ACTUAL:         2^(1/2)*EllipticPi(1,1/2*2^(1/2))

EXPECTED:       infinity

...............................................................................
BUG # 25 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  SPURIOUS CONVERGENCE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                LOOPED     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ERROR      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(sqrt(1-1/z^(3/2)), z=1..infinity);

ACTUAL:         1/12*I*Pi^(1/2)*2^(1/2)*(12/7/Pi^(1/2)*2^(1/2)*hypergeom([3/4,\
                1/4, 7/12],[3/2, 19/12],1)-24/Pi^(1/2)*2^(1/2)*hypergeom([1/12\
                ,-1/4,1/4],[1/2,13/12],1)+3/2*sin(5/12*Pi)*sec(1/12*Pi)*csc(1/\
                12*Pi)*2^(2/3)*Pi^(1/2)*GAMMA(7/12)/GAMMA(2/3)/GAMMA(11/12))

                0.3389019737e-10+0.*I

EXPECTED:       infinity

CHECK-UP:       evalf(Int(sqrt(1-1/z^(3/2)), z=1..10^10));

                9999999999.

The same problem with

int(sqrt(1-1/z^(5/3)), z=1..infinity);
int(sqrt(1-1/z^(7/4)), z=1..infinity);
int(sqrt(1-1/z^(6/5)), z=1..infinity);

...............................................................................
BUG # 26 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  SPURIOUS CONVERGENCE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(FresnelC(z)*ln(z), z=0..infinity);

ACTUAL:         1/4

EXPECTED:       infinity

CHECK-UP:       evalf(Int(FresnelC(z)*ln(z), z=0..infinity));

                Float(infinity)


                int(FresnelS(z)*ln(z), z=0..infinity);

ACTUAL:         1/2*(2-ln(2)+gamma+ln(Pi))/Pi

EXPECTED:       infinity

CHECK-UP:       evalf(Int(FresnelS(z)*ln(z), z=0..infinity));

                Float(infinity)

...............................................................................
BUG # 27 (int)

*********************************
***  INVALID Re/Im MAGNITUDE  ***
*********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                LOOPED     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(sqrt(sqrt(z))/(1+z^2),z=-infinity..infinity));

ACTUAL:         0. + 0.*I

EXPECTED:       Pi*sqrt(sqrt(2)/4+1/2)+Pi*I*sqrt(1/2-sqrt(2)/4)

CHECK-UP:       2.902453152+1.202235460*I

                evalf(Int(sqrt(sqrt(z))/(1+z^2),z=-infinity..infinity));

                2.902453152+1.202235460*I

The same problem with

                int(z^(1/5)/(1+z^2),z=-infinity..infinity);

...............................................................................
BUG # 28 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*********************************
***  INVALID Re/Im MAGNITUDE  ***
*********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 1      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(signum(ln(z)), z= -1..1);

ACTUAL:         0

EXPECTED:       -1+Pi/2+Pi^2*(2*BesselY(1,Pi)+StruveH(-1,Pi)-StruveH(1,Pi))/4+\
                I*(Pi^2*(-BesselY(0,Pi)+StruveH(0,Pi)))/2

                -1.267639165+.9349432435*I

COMMENT:        Alas, the Maple 8 numeric integrator cannot knock out this,

                evalf(Int(signum(ln(z)), z= -1..1));

                evalf(Int(signum(ln(z)), z= -1..1));

COMPARE:        MuPAD 2.5 numerical integration yields

                numeric::int(sign(ln(z)), z= -1..1);

                -1.267639165 + 0.9349432437*I

HINT:           plot(Re(signum(ln(z))), z= -1..1);
                plot(Im(signum(ln(z))), z= -1..1);

...............................................................................
BUG # 29 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 2      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 3      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(arccot(1/sin(z)), z=0..Pi/2);

ACTUAL:         1/2*dilog(1/(1+2^(1/2))*2^(1/2)+1/(1+2^(1/2))+I/(1+2^(1/2)))+1\
                /4*I*Pi*ln(-1-I)-1/4*I*Pi*ln(2^(1/2)-1+I)-1/4*I*Pi*ln(2^(1/2)+\
                1-I)+1/6*Pi^2-1/4*I*Pi*ln(-1+I)-1/2*dilog(1/(2^(1/2)-1)*2^(1/2\
                )-1/(2^(1/2)-1)+I/(2^(1/2)-1))+1/4*I*Pi*ln(2^(1/2)-1-I)-1/2*di\
                log(1/(1+2^(1/2))*2^(1/2)+1/(1+2^(1/2))-I/(1+2^(1/2)))+1/4*I*P\
                i*ln(2^(1/2)+1+I)+1/2*dilog(1/(2^(1/2)-1)*2^(1/2)-1/(2^(1/2)-1\
                )-I/(2^(1/2)-1))+1/2*dilog(1/(2^(1/2)-1)*2^(1/2))+1/2*dilog(1+\
                2/(2^(1/2)-1)-1/(2^(1/2)-1)*2^(1/2))+1/2*ln(1+2^(1/2))*ln(2-2^\
                (1/2))-1/2*ln(1+2^(1/2))*ln(2^(1/2)-1)-1/2*I*ln(1+2^(1/2))*Pi-\
                1/2*dilog(2/(1+2^(1/2))+1/(1+2^(1/2))*2^(1/2))+1/2*dilog(1/(1+\
                2^(1/2))*2^(1/2))

                5.780093050+.2e-8*I

EXPECTED:       -1/2*polylog(2,3-2*2^(1/2))+2*polylog(2,2^(1/2)-1)

CHECK-UP:

                evalf(Int(arccot(1/sin(z)), z=0..Pi/2));

                .8452908502

HINT:           plot(arccot(1/sin(z)), z=0..Pi/2);

The same problem with

                int(arccot(csc(z)), z=0..Pi/2);

...............................................................................
BUG # 30 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  SPURIOUS CONVERGENCE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      simplify(int(a^(log[2](z)), z=0..infinity));

ACTUAL:         0

EXPECTED:       undefined  or  int(a^(log[2](z)), z=0..infinity);

COMMENT:        int(1^(log[2](z)), z=0..infinity);

                infinity


EXAMPLE 2:      int(I^(log[2](z)), z=0..infinity);

ACTUAL:         0

EXPECTED:       undefined

...............................................................................
BUG # 31 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  SPURIOUS CONVERGENCE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(z)*arctan(sqrt(z)), z=0..infinity);

ACTUAL:         -1/2*Pi

EXPECTED:       infinity

CHECK-UP:       evalf(Int(ln(z)*arctan(sqrt(z)), z=0..infinity));

                Float(infinity)

...............................................................................
BUG # 32 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*****************************
***  SPURIOUS DIVERGENCE  ***
*****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      int(ln(1+z^(1/2))/(1+z^2), z = 0..infinity);

ACTUAL:         infinity*signum(1/2*sum(_R1*(ln(_R1)+ln(1/_R1))/(_R1^3-3*_R1^2\
                +3*_R1-1),_R1 = RootOf(2+_Z^4-4*_Z^3+6*_Z^2-4*_Z))-1/2*sum((ln\
                (_R1)+ln(1/_R1))/(_R1^3-3*_R1^2+3*_R1-1),_R1 = RootOf(2+_Z^4-4\
                *_Z^3+6*_Z^2-4*_Z)))

                evalf(%);

                Float(undefined)+Float(undefined)*I

EXPECTED:       1/2*Pi*ln(2^(3/4)+2^(1/4))-1/2*Catalan

CHECK-UP:       1.198673857

                evalf(Int(ln(1+z^(1/2))/(1+z^2),z = 0 .. infinity));

                1.198673857


EXAMPLE 2:      int(ln(1+1/z^(1/2))/(1+z^2),z = 0 .. infinity);

ACTUAL:         infinity*signum(1/2*sum(_R1*(ln(_R1)+ln(1/_R1))/(_R1^3-3*_R1^2\
                +3*_R1-1),_R1 = RootOf(2+_Z^4-4*_Z^3+6*_Z^2-4*_Z))-1/2*sum((ln\
                (_R1)+ln(1/_R1))/(_R1^3-3*_R1^2+3*_R1-1),_R1 = RootOf(2+_Z^4-4\
                *_Z^3+6*_Z^2-4*_Z)))

                evalf(%);

                Float(undefined)+Float(undefined)*I

EXPECTED:       1/2*Pi*ln(2^(3/4)+2^(1/4))-1/2*Catalan

CHECK-UP:       1.198673857

                evalf(Int(ln(1+1/z^(1/2))/(1+z^2),z = 0 .. infinity));

                1.198673857


EXAMPLE 3:      int(ln(z^(3/2)+1)/(1+z^3),z = 0 .. infinity);

ACTUAL:         signum(1/2*Sum(1,_alpha = RootOf(_Z^2+1))-1/2*Sum(_alpha^2,_al\
                pha = RootOf(_Z^4-_Z^2+1)))*infinity

                evalf(%);

                Float(undefined)+Float(undefined)*I

EXPECTED:       -(Pi*(Pi - 6*sqrt(3)*ln(2)))/18

CHECK-UP:       .7089185601

                evalf(Int(ln(z^(3/2)+1)/(1+z^3),z = 0 .. infinity));

                .7089185598

...............................................................................
BUG # 33 (int)

****************************
***  SPURIOUS undefined  ***
****************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG-2      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      int(1/abs(1-tan(z)), z=0..Pi/5);

ACTUAL:         undefined

EXPECTED:       Pi/10 - ln(- sqrt(5/8 - sqrt(5)/8) + sqrt(5)/4 + 1/4)/2

CHECK-UP:       1.068431525

                evalf(Int(1/abs(1-tan(z)), z=0..Pi/5));

                1.068431525


EXAMPLE 2:      int(1/abs(1+tan(z)), z=0..Pi/5);

ACTUAL:         undefined

EXPECTED:       1/2*ln(1+cot(3/10*Pi))+1/10*Pi-1/4*ln(1+cot(3/10*Pi)^2)

CHECK-UP:       .4812520226

                evalf(Int(1/abs(1+tan(z)), z=0..Pi/5));

                .4812520226

...............................................................................
BUG # 34 (int)

***********************************
***  BAD NUMERICAL INTEGRATION  ***
***********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                CANNOT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ERROR      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ERROR      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(sqrt(1+1/z^(3/2)), z=-1..1));

ACTUAL:         5.859030449+1.1610594455*I

EXPECTED:       7.303152458+2.657766004*I

                7.241889406 + 2.646626173*I  (Derive)

...............................................................................
BUG # 35 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************************
***  SPURIOUS NON-ZERO IMAGINARY PART  ***
******************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 2      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 2      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(sin(z)/(1+z)), z=0..Pi);

ACTUAL:         -Pi*ln(2)-I*Pi^2-ln(1+Pi)-Pi*ln(1+Pi)+Pi

                -4.921529636-9.869604404*I

EXPECTED:       -Pi*ln(2)-ln(1+Pi)-Pi*ln(1+Pi)+Pi

CHECK-UP:       -4.921529636

                evalf(Int(ln(sin(z)/(1+z)), z=0..Pi));

                -4.921529635

...............................................................................
BUG # 36 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************
***  SYSTEM ERROR  ***
**********************

REPRODUCIBLE    INTERMITTENTLY

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CRASHED    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(arcsin(1/arccos(z)), z=0..infinity);

ACTUAL:         unevaluated  or  `System error, `, "ran out of memory"

EXPECTED:       int(Re(arcsin(1/arccos(z))), z=0..1)-Infinity*I

...............................................................................
BUG # 37 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                UNDONE     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(sin(z)/(1+z)), z=0..infinity);

ACTUAL:         Error, (in limit/range) numeric exception: division by zero

EXPECTED:       -infinity+I*infinity

...............................................................................
BUG # 38 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

********************
***  WRONG SIGN  ***
********************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(z)*arctan(z), z=0..infinity);

ACTUAL:         -infinity

EXPECTED:       infinity

CHECK-UP:       evalf(Int(ln(z)*arctan(sqrt(z)), z=0..infinity));

                Float(infinity)

..............................................................................
BUG # 39 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  INVALID Im MAGNITUDE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(ln(z)*arctan(z)/(1+z^2)^2,z=-infinity..infinity));

ACTUAL:         -1.937892292*I

EXPECTED:       -1.152494129*I

ANSWER:         -1/16*I*Pi*(-4+Pi^2)

                -1.152494130*I

CHECK-UP:       evalf(Int(ln(z)*arctan(z)/(1+z^2)^2,z=-infinity..infinity));

                0.-1.152494129*I

...............................................................................
BUG # 40 (evalf)

*********************************
***  SLOWDOWN OF 14240 TIMES  ***
*********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ABSENT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR 1    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

It takes 213.6 seconds to calculate the following approximation. In Maple 7 it
takes only 0.015 seconds.

                time(evalf(hypergeom([1, 1, 5/4],[2, 7/4],1)));

ACTUAL:         213.6

EXPECTED:       0.015

...............................................................................
BUG # 41 (int)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CANNOT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(1+sin(z)), z=0..infinity);

ACTUAL:         Error, (in limit/range) invalid terms in sum

EXPECTED:       infinity

The same problem with

                int(ln(1+sin(z)^2), z=0..infinity);
                int(ln(1-sin(z)), z=0..infinity);
                int(ln(1+cos(z)), z=0..infinity);
                int(ln(1-cos(z)), z=0..infinity);
                int(ln(1-sin(z)^2), z=0..infinity);
                int(ln(1+cos(z)^2), z=0..infinity);
                int(ln(1-cos(z)^2), z=0..infinity);
                int(ln(1+sin(z)^2), z=0..infinity);

...............................................................................
BUG # 42 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(abs(sin(z)), z=-infinity..infinity);

ACTUAL:         undefined

EXPECTED:       infinity

...............................................................................
BUG # 43 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                LOOPED     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR 2    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ERROR 2    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR 1    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(arcsin(1/arccos(z)), z=0..1));

ACTUAL:         Error, (in simpl/simpl/ReIm/sum) too many levels of recursion

EXPECTED:       1.224555967 - 0.4729516698*I

CHECK-UP:       evalf(Int(arcsin(z)/z^2*sin(1/z),z=2/Pi..infinity));

                1.224555970-.4729517363*I

...............................................................................
BUG # 44 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

***********************************
***  SIMPLE INTEGRAL IS UNDONE  ***
***********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR 1    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ERROR 1    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

This integral is TOO simple to be left unprocessed.
I definitely feel, it is a BUG.


                int(Ci(z), z=0..infinity);

ACTUAL:         limit(z*Ci(z)-sin(z),z = infinity)

EXPECTED:       0

CHECK-UP:       evalf(Int(Ci(z), z=0..infinity));

                -.2e-12

...............................................................................
BUG # 45 (int)

*********************************
***  INVALID Re/Im MAGNITUDE  ***
*********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(sqrt(abs(z^3+1)),z=0..2));

ACTUAL:         2.144908076+.9220552755*I


EXPECTED:       12/5+2/5*3^(3/4)*EllipticK(1/4*2^(1/2)*3^(1/2)+1/4*2^(1/2))-1/\
                5*3^(3/4)*EllipticF(2*3^(1/4)/(1+3^(1/2)),1/4*2^(1/2)*3^(1/2)+\
                1/4*2^(1/2))-1/5*3^(3/4)*EllipticF(2*3^(3/4)/(3+3^(1/2)),1/4*2\
                ^(1/2)*3^(1/2)+1/4*2^(1/2))

CHECK-UP:       3.241309265

                evalf(Int(sqrt(abs(z^3+1)),z=0..2));

                3.241309263

...............................................................................
BUG # 46 (int)

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 2      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 2      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                BUG 1      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(1/(1+(-1+z)^2)*arctan(z), z=0..infinity));

ACTUAL:         .7101324486+0.*I

EXPECTED:       -1/4*arctan(1/3)^2-1/2*Pi*arctan(1/3)+1/16*ln(5)^2 -1/8*ln(2)*\
                ln(5)+1/4*dilog(2/5-1/5*I)+1/4*dilog(2/5+1/5*I)+15/64*Pi^2

CHECK-UP:       2.152744571+0.*I

                evalf(Int(1/(1+(-1+z)^2)*arctan(z), z=0..infinity));

                2.152744570

...............................................................................
BUG # 47 (fourier/invfourier)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

********************************
***  BAD fourier/invfourier  ***
********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                UNDONE     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                invfourier(fourier(ln(1+1/z),z,p),p,z);

ACTUAL:         0

EXPECTED:       ln(1+1/z)

...............................................................................
BUG # 48 (fourier/invfourier)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

********************************
***  BAD fourier/invfourier  ***
********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                UNDONE     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                invfourier(fourier(ln(z),z,p),p,z);

ACTUAL:         -infinity/Pi

EXPECTED:       ln(z)

The same problem with

                fourier(ln(1+z),z,p);
                fourier(ln(1-z),z,p);
                fourier(ln(z)/(1-z^2),z,p);
                fourier(ln(1+1/z),z,p);
                fourier(ln(1-1/z),z,p);
                fourier(ln(1-1/z^2),z,p);
                fourier(ln(z)*Heaviside(z),z,p);

...............................................................................
BUG # 49 (fourier)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                UNDONE     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                UNDONE     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                UNDONE     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                fourier(ln(z)*ln(1/z), z, p);

ACTUAL:         Error, (in inttrans/normalize/distributional) unable to
                evaluate sign

The same problem with

                fourier(ln(z)*ln(-z), z, p);
                fourier(ln(1+z)*ln(1-z), z, p);
                fourier(ln(z)/(1+z), z, p);
                fourier(ln(z)/(1-z), z, p);
                fourier(ln(z)/(1+z^2), z, p);
                fourier(ln(z)/(1-z^2), z, p);
                fourier(ln(z)/(1+z^3), z, p);
                fourier(ln(z)/(1-z^3), z, p);

...............................................................................
BUG # 50 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 2      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 2      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994


                evalf(int(sqrt(abs(z-1)*(z^2+1)),z=0..2));

ACTUAL:         undefined

EXPECTED:

...............................................................................
BUG # 51 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*********************************
***  INVALID Re/Im MAGNITUDE  ***
*********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 2      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 2      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994


                int(sqrt(-z^3+z^2-z+1),z=0..1):

                evalf(%,25);

ACTUAL:         .7282824328479719343655894-.30452847612989774120152e-2*I

EXPECTED:       .7356418194982207194404737

ANSWER:         2/15+8/15*(2+2*I)^(1/2)*EllipticF(1/2*(2-2*I)^(1/2),1/2*2^(1/2\
                )+1/2*I*2^(1/2))-4/15*(2+2*I)^(1/2)*EllipticE(1/2*(2-2*I)^(1/2\
                ),1/2*2^(1/2)+1/2*I*2^(1/2))+4/15*I*(2+2*I)^(1/2)*EllipticE(1/\
                2*(2-2*I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))-4/15*I*(2+2*I)^(1/2\
                )*EllipticF(1/2*(2-2*I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))

CHECK-UP:       evalf(%,25);

                .7356418194982207194404731+0.*I

                evalf(Int(sqrt(-z^3+z^2-z+1),z=0..1),25);

                .7356418194982207194404737

...............................................................................
BUG # 52 (laplace)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************


REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                laplace(ln(z)^2/(1+z),z,p);

ACTUAL:         Error, (in int/cook/ngritty) wrong number (or type) of
                parameters in function diff

EXPECTED:       1/6*Pi^2*exp(p)*Ei(1,p)+gamma^2*exp(p)*Ei(1,p)+2*exp(p)*gamma*\
                ln(p)*Ei(1,p)+2*exp(p)*gamma*MeijerG(3,0,p)*p+exp(p)*ln(p)^2*\
                Ei(1,p)+2*exp(p)*ln(p)*MeijerG(3,0,p)*p+2*exp(p)*MeijerG(4,0,p\
                )*p

...............................................................................
BUG # 53 (plot)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can draw this graph correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

***********************
***  INVALID GRAPH  ***
***********************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                plot((1 - signum(z*(z + 1)))/sqrt(z + 1),z=0..10);

ACTUAL:         A vertical line from y = 0 to y = 0.55

EXPECTED:       The vertical line is absent.

COMMENT:        Mathematica 4.2, MuPAD 2.5 and Derive 5.06 handle it.

DRAW ME:        Plot[(1 - Sign[z*(z + 1)])/Sqrt[z + 1], {z, 0, 10}]
                plotfunc2d((1 - sign(z*(z + 1)))/sqrt(z + 1), z=0..10);
                (1 - SIGN(z*(z + 1)))/SQRT(z + 1)

...............................................................................
BUG # 54 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*************************
***  INVALID Re SIGN  ***
*************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The sign of the output must be opposite.

The value of the integral must be negative as the integrand is negative
everywhere over the integration region.

                evalf(int(1/(sqrt(z-1)*sqrt(z-2)*sqrt(3-z)), z=0..1));

ACTUAL:         1.168165683

EXPECTED:       -1.168165683

CHECK-UP:       evalf(Int(1/(sqrt(z-1)*sqrt(z-2)*sqrt(3-z)), z=0..1));

                -1.168165683

HINT:           plot(1/(sqrt(z-1)*sqrt(z-2)*sqrt(3-z)), z=0..1)

...............................................................................
BUG # 55 (invlaplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*************************
***  INVALID Re SIGN  ***
*************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                UNDONE     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The output of the Laplace transform is correct.

                with(inttrans):
                laplace(1/sqrt(1+z), z, p), p, z);

                (Pi/p)^(1/2)*exp(p)*erfc(p^(1/2))    #  OK

However, the output of the inverse Laplace transform has the wrong sign.

The easiest way to see it is to draw

                original := 1/sqrt(1+z):

                plot(original + invlaplace(laplace(original,z,p),p,z),z=0..10);

which yields the straight line  y = 0  (in fact, Maple 8 explodes it into
a picket fence of vertical lines) instead of the curve  y = 2/sqrt(1+z).

...............................................................................
BUG # 56 (invlaplace)

*************************
***  INVALID Re SIGN  ***
*************************

REGRESSION      YES

REPRODUCIBLE    INTERMITTENTLY

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The output of the Laplace transform is correct.

                with(inttrans):
                laplace(arccosh(1-z), z, p);

                1/p*exp(-p)*BesselK(0,-p)            #  OK

However, the output of the inverse Laplace transform has the wrong sign.

The easiest way to see it is to draw

                original := arccosh(1-z):

                plot(original + invlaplace(laplace(original,z,p),p,z),z=0..10);

which yields the straight line  y = 0  (in fact, Maple 8 explodes it into
a picket fence of vertical lines) instead of the curve  y = 2*arccosh(1-z).

                invlaplace(laplace(original,z,p),p,z);

EXPECTED:       2*ln(-1/2*I*2^(1/2)*(z^(1/2)+(z-2)^(1/2)))

...............................................................................
BUG # 57 (int)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 1      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 2      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 2      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(sqrt(abs(z^2-1)*(z^2+1)),z=0..2);

ACTUAL:         Error, (in signum/main) too many levels of recursion

EXPECTED:       1/4*Beta(1/4,3/2)+2/3*5^(1/2)*3^(1/2)-1/3*2^(1/2)*EllipticF(1/\
                2*3^(1/2),1/2*2^(1/2))

CHECK-UP:       2.917461861

                evalf(Int(sqrt(abs(z^2-1)*(z^2+1)),z=0..2));

                2.917461860

The same problem with

                int(sqrt(abs(z^2-1)*(z^2+1)),z=-2..2);
                int(sqrt(abs(z^2-1)*(z^2+1)),z=-infinity..infinity);

...............................................................................
BUG # 58 (evalf)

**************************************
***  NUMERIC VALUE IS UNAVAILABLE  ***
**************************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 1      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(sqrt(1-1/z^(4/3)), z=0..1));

ACTUAL:         Int((1.-1./z^(4/3))^(1/2),z = 0. .. 1.)

EXPECTED:       2.622057554*I

...............................................................................
BUG # 59 (fourier/invfourier)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 1      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1      Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 1      Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans);
                invfourier(fourier(ln(z)*ln(1/z), z, p), p, z);

ACTUAL:         Error, (in inttrans/normalize/distributional) unable to
                evaluate sign

EXPECTED:       ln(z)*ln(1/z)

The same problem with

                invfourier(fourier(ln(1+z)*ln(1-z), z, p), p, z);

...............................................................................
BUG # 60 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(erf(1+z/exp(z)), z=-infinity..infinity);

ACTUAL:         undefined

                int(erf(1+z/exp(z)), z=-infinity..infinity,
                'CauchyPrincipalValue');

ACTUAL:         undefined

EXPECTED:       -infinity

CHECK-UP:       evalf(Int(erf(1+z/exp(z)), z=-10^6..10^6));

                -157298.1589

HINT:           plot(evalf(Int(erf(1+z/exp(z)), z=-a..a)),a=0..20);

...............................................................................
BUG # 61 (invlaplace)

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ABSENT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The output for the inverse Laplace transform is invalid.

                with(inttrans):
                laplace(sqrt(1+z), z, p):
                invlaplace(%,p,z);

ACTUAL:         1+sqrt(Pi)/2*int(2*Heaviside(_U1-1)*Heaviside(1+z-_U1)*sqrt(1+\
                z-_U1)/(Pi^(3/2)*_U1*(_U1-1)), _U1=0..z)

                evalf(subs(z=1, %));

                1.              #  it should be 1.414213562, evalf(sqrt(2))

EXPECTED:       1-1/(1+z)+1/(1+z)/z^(1/2)/(1/(-1-z))^(1/2)/(1+1/z*(-1-z))^(1/2\
                )-1/(1+z)*z+1/(1+z)*z^(1/2)/(1/(-1-z))^(1/2)/(1+1/z*(-1-z))^(1\
                /2)

...............................................................................
BUG # 62 (invlaplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 1      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The output for the inverse Fourier transform is invalid.

                with(inttrans):
                invfourier(fourier(abs(z)*sin(z)*ln(z), z, p), p, z);

ACTUAL:         undefined/Pi

EXPECTED:       abs(z)*sin(z)*ln(z)

...............................................................................
BUG # 63 (invfourier)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 1      Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1      Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                fourier(sin(5*z)*cos(2*z)*ln(z), z, p);
                invfourier(%, p, z);

ACTUAL:         Error, (in inttrans/normalize/exp/classsimp) unable to
                compute coeff

EXPECTED:       sin(5*z)*cos(2*z)*ln(z)

...............................................................................
BUG # 64 (evalf)

****************
***  LOOPED  ***
****************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                CRASHED    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR 1    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ERROR 1    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                LOOPED     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(ln(1+z)*ln(1-z^3), z=-infinity..infinity));

ACTUAL:         Being the single task, after 2 hours the input keeps running

EXPECTED:       a large number like .3178376964e^1008 + .2892257128e1005*I

...............................................................................
BUG # 65 (interface)

**************************************
***  INDICATORS ARE NOT REFRESHED  ***
**************************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ABSENT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(ln(1+z)*ln(1-z^3), z=-infinity..infinity));

ACTUAL:         The same report 'Timer: 3.3s' is shown for 2 hours

EXPECTED:       The reading of the indicator is changed

...............................................................................
BUG # 66 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************************
***  SPURIOUS NON-ZERO IMAGINARY PART  ***
******************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(int(ln(1+z)*ln(1-z^2), z=-1..1));

ACTUAL:         4*ln(2)^2-8*ln(2)+4*I*Pi*ln(2)-4*I*Pi+8-1/3*Pi^2

                1.086766477-3.856026256*I

EXPECTED:       4*ln(2)^2-8*ln(2)+8-1/3*Pi^2

CHECK-UP:       1.086766477

                evalf(Int(ln(1+z)*ln(1-z^2), z=-1..1));

                1.086766477

...............................................................................
BUG # 67 (invlaplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The value of the inverse Laplace transformation of  laplace(BesselK(1, sqrt(z)\
), z, p);  is incorrect. Spurious factor 1/64*Pi is present in the answer.

                with(inttrans):
                laplace(BesselK(1, sqrt(z)), z, p);

                1/8*Pi^(1/2)/p^(3/2)*exp(1/8/p)*(BesselK(1,1/8/p)-   #  VALID
                BesselK(0,1/8/p))                                    #  VALID

                invlaplace(%, p, z);

ACTUAL:         1/64*Pi*BesselK(1,z^(1/2))                           #  INVALID

EXPECTED:       BesselK(1,z^(1/2))

...............................................................................
BUG # 68 (laplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************************
***  SPURIOUS NON-ZERO IMAGINARY PART  ***
******************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                laplace(1/(z^2-1), z, p);

ACTUAL:         -I*(I*Ci(I*p)*sinh(p)-Ssi(I*p)*cosh(p))

                evalf(subs(p=1/2,%));

                -.5992044654-.9527361321*I

EXPECTED:       The imaginary part of the answer = 0

...............................................................................
BUG # 69 (fourier)

****************
***  LOOPED  ***
****************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ABSENT     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                BUG 1      Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                fourier(sin(z)/(1+z^3),z,p);

ACTUAL:         Being the single task, after 7.4 hours the input keeps running

EXPECTED:       -1/2*I*(1/3*I*exp(I*(-1+p))*Pi*(Heaviside(1-p)-Heaviside(-1+p)\
                )+exp(-1/2*I*(-1+p))*(1/3*I*(-1-I*3^(1/2))*exp(1/2*3^(1/2)*(-1\
                +p))*Pi*Heaviside(1-p)-1/3*I*(-1+I*3^(1/2))*exp(-1/2*3^(1/2)*(\
                -1+p))*Pi*Heaviside(-1+p))) + 1/2*I*(1/3*I*exp(I*(1 + p))*Pi*(\
                Heaviside(-1-p)-Heaviside(1+p))+exp(-1/2*I*(1+p))*(1/3*I*(-1-I\
                *3^(1/2))*exp(1/2*(1+p)*3^(1/2))*Pi*Heaviside(-1-p)-1/3*I*(-1+\
                I*3^(1/2))*exp(-1/2*(1+p)*3^(1/2))*Pi*Heaviside(1+p)))

...............................................................................
BUG # 70 (laplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************************
***  SPURIOUS NON-ZERO IMAGINARY PART  ***
******************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The imaginary part of the output must be equal to zero.

                with(inttrans):
                laplace(exp(-z)/(1-z^2), z,p);

ACTUAL:         I*(I*Ci(I*(1+p))*sinh(1+p)-Ssi(I*(1+p))*cosh(1+p))

                evalf(subs(p=1,%));

                .515905660+.212584166*I

...............................................................................
BUG # 71 (laplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************************
***  SPURIOUS NON-ZERO IMAGINARY PART  ***
******************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The imaginary part of the output must be equal to zero.

                with(inttrans):
                laplace(sqrt(z)/(1-z), z,p);

ACTUAL:         -(Pi/p)^(1/2)+I*Pi*exp(-p)*erfc((-p)^(1/2))

                evalf(subs(p=1,%));

                .134988344+1.155727338*I

...............................................................................
BUG # 72 (laplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************************
***  SPURIOUS NON-ZERO IMAGINARY PART  ***
******************************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The imaginary part of the output must be equal to zero.

                with(inttrans):
                laplace(sec(z), z, p);

ACTUAL:         -I*p*Sum(2*n/(p^2+n^2)*exp(-1/2*I*n*Pi),n=0..infinity)-1/p^2

                evalf(subs(p=1,%));

                -1.626020143+.5161277204*I

...............................................................................
+++
BUG # 73 (laplace)

**********************************
***  FAILURE AFTER 266 minutes ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CANNOT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                laplace(exp(-z^3)/z^10, z, p);

ACTUAL:         int(int(int(int(int(int(int(int(int(int(laplace(exp(-z^3), z, \
                _U1),_U1=_U2..infinity),_U2=_U3..infinity),_U3=_U4..infinity),\
                _U4=_U5..infinity),_U5=_U6..infinity),_U6=_U7..infinity), _U7=\
                _U8..infinity),_U8=_U9..infinity),_U9=_U10..infinity),  _U10= \
                p..infinity)

EXPECTED:       If Maple cannot return an answer, it should be recognized
                faster.

...............................................................................
BUG # 74 (invlaplace)

******************************
***  INVALID Re MAGNITUDE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                BUG 1     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The Laplace transform is  v a l i d.

                with(inttrans):
                laplace(sqrt(1+z), z, p);

                1/p^(3/2)*exp(p)*(p^(1/2)*exp(-p)+1/2*Pi^(1/2)*erfc(p^(1/2)))

However, the inverse Laplace transform is  i n v a l i d.

                invlaplace(%,p,z);

ACTUAL:         1+sqrt(Pi)/2*int(2*Heaviside(_U1-1)*Heaviside(1+z-_U1)*sqrt(1+\
                z-_U1)/(Pi^(3/2)*_U1*(_U1-1)), _U1=0..z)

                evalf(subs(z=1,%));

                1.

EXPECTED:       1-1/(1+z)-1/(1+z)*z+1/(1+z)/(1+1/(-1-z)*z)^(1/2)+1/(1+z)*z/(1+\
                1/(-1-z)*z)^(1/2)

CHECK-UP:       evalf(subs(z=1,%));

                1.414213562

                evalf(sqrt(1+1));

                1.414213562

...............................................................................
BUG # 75 (laplace)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                laplace(sin(z)*sqrt(z),z,p);

ACTUAL:         Error, (in tablelook) wrong number (or type) of parameters
                in function iquo

EXPECTED:       1/2*Pi^(1/2)/(p^2+1)^(3/4)*sin(3/2*arctan(1/p))

COMMENT:        Mathematica 4.2 handles it.

The same problem with

                laplace(sqrt(z)*cos(z),z,p);
                laplace(sqrt(z)*sin(2*z),z,p);
                laplace(sqrt(z)*cos(2*z),z,p);
                laplace(sqrt(z)*sin(z+1),z,p);
                laplace(sqrt(z)*sin(z+c),z,p);
                laplace(sqrt(z)*sin(c*z),z,p);

                laplace(z^(1/3)*sin(z),z,p);
                laplace(z^(1/3)*cos(z),z,p);
                laplace(z^(1/4)*sin(z),z,p);
                laplace(z^(1/4)*cos(z),z,p);

                laplace(z^(1/3)*sin(c*z),z,p);

...............................................................................
+++
BUG # 76 (laplace)

****************************
***  MEANINGLESS OUTPUT  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The answer does NOT depend on p though it must depend.

                with(inttrans):
                laplace(frac(z), z, p);

ACTUAL:         (exp(-1/N*t)*t+exp(-1/N*t)*N-N)/t^2/(exp(-1/N*t)-1)

EXPECTED:       The output depends on p only.

...............................................................................
BUG # 77 (invlaplace)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans);
                invlaplace(exp(-p*Pi)/(p*(-1+exp(-p*Pi))),p,z);

ACTUAL:         Error, (in inttrans/simpfloor) unable to evaluate sign

EXPECTED:       Heaviside(z-Pi)*floor(-(z-Pi)/Pi)

The same problem with

                invlaplace(1/(p*(1+exp(-p*Pi))),p,z);
                invlaplace(1/(p*(1-exp(-p*Pi))),p,z);
                invlaplace(1/(p*(1-exp(p*Pi))),p,z);
                invlaplace(exp(-p*Pi)/(p*(1+exp(-p*Pi))),p,z);
                invlaplace(exp(-p*Pi/2)/(p*(1+exp(-p*Pi))),p,z);
                invlaplace(exp(-p*Pi/2)/(p*(-1+exp(-p*Pi))),p,z);

...............................................................................
BUG # 78 (laplace)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this expression correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                BUG 2     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                with(inttrans):
                laplace(BesselY(0, sqrt(z)), z, p);

ACTUAL:         Error, (in cot) numeric exception: division by zero

EXPECTED:       1/p/Pi*exp(-1/4/p)*Ei(1/4/p)

The same problem with

                laplace(BesselY(k, sqrt(z)), z, p);

where k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

...............................................................................
BUG # 79 (laplace)

*****************************
***  STRANGE LIMITATIONS  ***
*****************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

These 3 examples work fine.

                with(inttrans):
                laplace(z*sin(z),z,p):
                invlaplace(%, p, z);

                z*sin(z)

                laplace(z^2*sin(z),z,p):
                invlaplace(%, p, z);

                z^2*sin(z)

                laplace(z^3*sin(z),z,p):
                invlaplace(%, p, z);

                z^3*sin(z)

However, the next example does not work.

                laplace(z^4*sin(z),z,p):
                invlaplace(%, p, z);

ACTUAL:         24*invlaplace(1/(p^2+1)^(5/2)*sin(5*arctan(1/p)),p,z)

EXPECTED:       z^4*sin(z)

The same problem with

                laplace(z^k*sin(z),z,p):
                invlaplace(%, p, z);

where k = 5, 6, 7, 8, 9, 10.

...............................................................................
BUG # 80 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CANNOT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      int(sqrt(1+cos(z)), z=0..infinity);

ACTUAL:         undefined

EXPECTED:       infinity

CHECK-UP:       evalf(Int(sqrt(1+cos(z)), z=0..1000));

                900.7628495


EXAMPLE 2:      int(sqrt(1+sin(z)), z=0..infinity);

ACTUAL:         undefined

EXPECTED:       infinity

CHECK-UP:       evalf(Int(sqrt(1+sin(z)), z=0..1000));

                900.6076621

...............................................................................
BUG # 81 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CRASHED   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CRASHED   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      int(sqrt(1+sin(z)^2), z=0..infinity);

ACTUAL:         Error, (in gcd/doit) too many levels of recursion

EXPECTED:       infinity

CHECK-UP:       evalf(Int(sqrt(1+sin(z)^2), z=0..1000));

                1215.912321


EXAMPLE 2:      int(sqrt(1+cos(z)^2), z=0..infinity);

ACTUAL:         Error, (in gcd/doit) too many levels of recursion

EXPECTED:       infinity

CHECK-UP:       evalf(Int(sqrt(1+cos(z)^2), z=0..1000));

                1216.104119

...............................................................................
BUG # 82 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(Ci(z)), z=1..infinity);

ACTUAL:         Error, (in limit/range) numeric exception: division by zero

EXPECTED:       -infinity+infinity*I

...............................................................................
BUG # 83 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*********************************
***  INVALID Re/Im MAGNITUDE  ***
*********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 1     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 1     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(sqrt(abs(sqrt(z) - 1)), z= -1..1);

ACTUAL:         4/3*(1-I)^(1/2)+4/15*I*(1-I)^(1/2)

                1.586269446-.3138040504*I

EXPECTED:       8*2^(1/4)/5 - 4/15

                1.636064717

CHECK-UP:       evalf(Int(sqrt(abs(sqrt(z) - 1)), z= -1..1));

...............................................................................
BUG # 84 (plot)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can draw this graph correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

***********************
***  INVALID GRAPH  ***
***********************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

EXAMPLE 1:      plot(sin(z),z=10^10..infinity);

ACTUAL:         A vertical line at infinity

EXPECTED:       A warning message like  'Unable show the graph. Try THIS or
                THAT' is shown where THIS and THAT are actions proposed to
                the user.


EXAMPLE 2:      plot(sin(z),z=10^7..infinity);

ACTUAL:         4 vertical lines connected by 3 obliques.

EXPECTED:       A warning message like  'Unable show the graph. Try THIS or
                THAT' is shown where THIS and THAT are actions proposed to
                the user.


EXAMPLE 3:      plot(sin(z),z=10^10..10^45);

ACTUAL:         Only the axes are shown.

EXPECTED:       A warning message like  'Unable show the graph. Try THIS or
                THAT' is shown where THIS and THAT are actions proposed to
                the user.

...............................................................................
BUG # 85 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculute this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  STRANGE LIMITATION  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

Consider        int(Pi/2-arctan(z^k), z=0..infinity);

Maple 8 can calculate correctly the integral at k = 0, 1, 2, 3, 4, 5, 6, 8, 10.
However, for k = 7 and k = 9 it, unexpectedly, cannot do it.


EXAMPLE 1:      int(Pi/2-arctan(z^7), z=0..infinity);

ACTUAL:         int(Pi/2-arctan(z^7), z=0..infinity);

EXPECTED:       (sin(3*Pi/14)*(4*Pi*sin(Pi/14)/7+2*Pi/7)-2*Pi*cos(Pi/7)*sin(3*\
                Pi/14)/7)/cos(3*Pi/14) - cos(Pi/7)*(4*Pi/(7*cos(Pi/14))-12*Pi*\
                sin(3*Pi/14)/(7*sin(Pi/7))+(6*Pi/7-6*Pi*sin(Pi/14)/7)/sin(Pi/7\
                ))+(Pi/7-2*Pi*sin(Pi/14)/7)/cos(Pi/14)

CHECK-UP:       1.611192283

                evalf(Int(Pi/2-arctan(z^7), z=0..infinity));

                1.611192281


EXAMPLE 2:      int(Pi/2-arctan(z^9), z=0..infinity);

ACTUAL:         int(Pi/2-arctan(z^9), z=0..infinity);

EXPECTED:       -1/18*(-1)^(5/9)*(9*I-2*(-1)^(1/18) +8*(-1)^(7/18)+4*(-1)^(13/\
                18)+3*3^(1/2)-6*(-1)^(4/9)*3^(1/2))*Pi

CHECK-UP:       1.595028393+.3418939372e-9*I

                evalf(Int(Pi/2-arctan(z^9), z=0..infinity));

                1.595028392

...............................................................................
BUG # 86 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculute this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  SPURIOUS CONVERGENCE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(z)^2*sin(z), z = -infinity..infinity);

ACTUAL:         Pi^2+2*I*Pi*gamma

EXPECTED:       undefined

...............................................................................
BUG # 87 (evalf)

**************************************
***  NUMERIC VALUE IS UNAVAILABLE  ***
**************************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                UNDONE    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

The answer involves terms like  D[1,1](LommelS1)(1/2,1/2,1) .

                evalf(subs(a=1,int(ln(z)^2*sin(z), z = 0..a)));

ACTUAL:         .3011686789*D[1,1](LommelS1)(1/2,1/2,1)+
                .4207354923*D[1](LommelS1)(3/2,3/2,1)-
                .4207354924*D[1,1](LommelS1)(3/2,3/2,1)+.1606255735

EXPECTED:       .2448680576

CHECK-UP:       evalf(Int(ln(z)^2*sin(z), z = 0..1));

                .2448680576

...............................................................................
BUG # 88 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(abs(1+sin(z)), z=-I*infinity..I*infinity);

ACTUAL:         Error, (in limit) invalid limiting point

EXPECTED:       I*infinity

CHECK-UP:       evalf(Int(abs(1+sin(z)), z=-I*10..I*10));

                22026.46575*I

...............................................................................
BUG # 89 (evalf)

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ERROR 1   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ERROR 1   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                evalf(Int(ln(Ci(z)), z=1..4));

ACTUAL:         Error, (in evalf/int) cannot assume on a constant object

EXPECTED:       -5.110609401+1.934654260*I

...............................................................................
BUG # 90 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

This works fine.

                int(1/(1 + I)^2, z = -I*infinity..I*infinity);

                infinity

However, this invokes an error.

                int(1/sqrt(z + I), z = -I*infinity..I*infinity);

ACTUAL:         Error, (in limit) invalid limiting point

EXPECTED:       undefined

                evalf(Int(1/sqrt(z + I), z = -I*infinity..I*infinity));

                Float(undefined)+0.*I


The same problem with

                int(1/z^2, z = 1..I*infinity);
                int(1/z, z = 1..I*infinity);
                int(z^sqrt(2), z=0..I*infinity);
                int(z^sqrt(2), z=-I*infinity..infinity);

...............................................................................
BUG # 91 (limit)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this limit correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                expr := z*(sin(z)*BesselJ(0,z)-cos(z)*BesselJ(1,z));

                limit(expr, z=infinity);

ACTUAL:         undefined

EXPECTED:       infinity

CHECK-UP:       evalf(limit(z*(sin(z)*BesselJ(0,z)-cos(z)*BesselJ(1,z)),
                z=10^10));

                56418.95836

HINT:           plot(expr, z=0..100);

...............................................................................
BUG # 92 (limit)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this limit correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  INVALID Im MAGNITUDE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                limit(exp(-1 + I*z) + exp(1 - I*z), z = infinity);


ACTUAL:         -exp(-1)-I*exp(-1)-exp(1)-I*exp(1) .. exp(-1)+I*exp(-1)+exp(1)\
                +I*exp(1)

                -3.086161269-3.086161269*I .. 3.086161269+3.086161269*I


EXPECTED:       -2*cosh(1) - I*2*sinh(1) .. 2*cosh(1) + I*2*sinh(1)

                -3.086161270-2.350402388*I .. 3.086161270+2.350402388*I


HINT:           plot(Im(exp(-1 + I*z) + exp(1 - I*z)), z = 1000000..1000200);

...............................................................................
BUG # 93 (plot)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can draw this graph correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

***********************
***  INVALID GRAPH  ***
***********************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                BUG 1     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                plot(abs(cos(z) + I*sin(z)) - 1, z= -1..1);

ACTUAL:         Spurious vertical lines near  z = 0.4 .

EXPECTED:       The straight line y = 0.


COMPARE 1:      Derive 5.05 (You may wish to use a free trial version at
                http://www.derive.com)

                ABS(COS(z) + #I*SIN(z)) - 1


COMPARE 2:      MuPAD 2.5   (You may wish to use a free trial version at
                http://www.mupad.com)

                plotfunc2d(abs(cos(z) + I*sin(z)) - 1, z= -1..1);

...............................................................................
BUG # 94 (plot)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can draw this graph correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

***********************
***  INVALID GRAPH  ***
***********************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                BUG 1     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                plot(-3 + abs((-1 + (1 + 6*(cos(z) + I*sin(z)))/(1 +3*(cos(z)+\
                I*sin(z))))/(-2 + (1 + 6*(cos(z) + I*sin(z)))/(1 + 3*(cos(z) +\
                I*sin(z))))), z= -2..2);

ACTUAL:         A complex-looking shape filled with hundreds vertical lines.

EXPECTED:       The straight line y = 0.


COMPARE 1:      Derive 5.05 (You may wish to use a free trial version at
                http://www.derive.com)

                -3+ABS((-1+(1+6*(COS(z)+#i*SIN(z)))/(1+3*(COS(z)+#i*SIN(z))))/~
                (-2+(1+6*(COS(z)+#i*SIN(z)))/(1+3*(COS(z)+#i*SIN(z)))))


COMPARE 2:      MuPAD 2.5   (You may wish to use a free trial version at
                http://www.mupad.com)

                plotfunc2d(-3+abs((-1 + (1 +6*(cos(z)+I*sin(z)))/(1+3*(cos(z)+\
                I*sin(z))))/(-2 + (1 + 6*(cos(z) + I*sin(z)))/(1 + 3*(cos(z) +\
                I*sin(z))))), z= -2..2);

...............................................................................
BUG # 95 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**********************************
***  ERROR MESSAGE IS INVOKED  ***
**********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                CANNOT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                BUG 1     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(Beta(1/z,-1/2), z=0..infinity);

ACTUAL:         Error, (in expand/Psi) too many levels of recursion

EXPECTED:       infinity

CHECK-UP:       evalf(Int(Beta(1/z,-1/2), z=0..10^100));

                .5000000000e200

The same problem with

                int(Beta(1/z^(1/2),-1/2), z=0..infinity);

...............................................................................
BUG # 96 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

***********************************
***  SIMPLE INTEGRAL IS UNDONE  ***
***********************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                CANNOT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ERROR     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

This integral is TOO simple to be left unprocessed.

                int(1/(z + sqrt(1-z)), z=0..1);

ACTUAL:         2/5*5^(1/2)*Re(arctanh(3/5*5^(1/2)))-1/2*I*Pi-1/2*ln(5+5^(1/2)\
                )+1/2*ln(-5-5^(1/2))+limit(1/2*ln(z^2-1+z)+1/5*5^(1/2)*arctanh\
                (1/5*(2*z+1)*5^(1/2))-1/2*ln(- z + (1-z)^(1/2)) - 1/5*5^(1/2)*\
                arctanh(1/5*(2*(1-z)^(1/2)+1)*5^(1/2))+1/2*ln(-z-(1-z)^(1/2))-\
                1/5*5^(1/2)*arctanh(1/5*(2*(1-z)^(1/2)-1)*5^(1/2)),z = RootOf(\
                _Z^2-1+_Z,.6180339887),left)+limit(-1/2*ln(z^2-1+z)-1/5*5^(1/2\
                )*arctanh(1/5*(2*z+1)*5^(1/2))+1/2*ln(-z+(1-z)^(1/2))+1/5*5^(1\
                /2)*arctanh(1/5*(2*(1-z)^(1/2)+1)*5^(1/2))-1/2*ln(-z-(1-z)^(1/\
                2))+1/5*5^(1/2)*arctanh(1/5*(2*(1-z)^(1/2) - 1)*5^(1/2)), z = \
                RootOf(_Z^2-1+_Z,.6180339887),right)

                evalf(%);

                .9779728648+3.844074127*I+limit(-1/2*ln(z^2-1+z)-1/5*5^(1/2)*a\
                rctanh(1/5*(2*z+1)*5^(1/2))+1/2*ln(-z+(1-z)^(1/2))+1/5*5^(1/2)\
                *arctanh(1/5*(2*(1-z)^(1/2)+1)*5^(1/2))-1/2*ln(-z-(1-z)^(1/2))\
                +1/5*5^(1/2)*arctanh(1/5*(2*(1-z)^(1/2)-1)*5^(1/2)),z = RootOf\
                (_Z^2-1+_Z,.6180339887),right)


EXPECTED:       sqrt(5)*ln(3*sqrt(5)/2+7/2)/5

CHECK-UP:       .8608178820

                evalf(Int(1/(z + sqrt(1-z)), z=0..1));

                .8608178819

...............................................................................
BUG # 97 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

****************************
***  SPURIOUS undefined  ***
****************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 1     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                BUG 2     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                BUG 2     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(abs(1,tan(z)-1)*(1+tan(z)^2)/(tan(z)-1)^2,z=0..Pi/5);

ACTUAL:         undefined

EXPECTED:       (5-2*5^(1/2))^(1/2)/((5-2*5^(1/2))^(1/2)-1)

                -2.656875748

CHECK-UP:       evalf(Int(abs(1,tan(z)-1)*(1+tan(z)^2)/(tan(z)-1)^2,z=0..Pi/5))

                -2.656875757

...............................................................................
BUG # 98 (int)

******************************
***  SPURIOUS CONVERGENCE  ***
******************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                BUG 1     Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994


                int(ln(z)^2/sqrt(1+z), z=0..infinity);

ACTUAL:         -16-4/3*Pi^2+16*ln(2)-8*ln(2)^2

                -21.91274176

EXPECTED:       infinity

CHECK-UP:       evalf(Int(ln(z)^2/sqrt(1+z), z=0..infinity));

                Float(infinity)

The same problem with

                int(ln(z)^(2*k)/sqrt(1+z), z=0..infinity);

where k = 2, 3, 4, 5,  and with

                int(ln(z)^(2*k)/(1+z)^(1/3), z=0..infinity);

where k = 1, 2, 3, 4, 5.

...............................................................................
BUG # 99 (int)

****************************
***  SPURIOUS undefined  ***
****************************

REGRESSION      YES

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(ln(z)^2/sqrt(1+z^2), z=0..infinity);

ACTUAL:         undefined

EXPECTED:       infinity

CHECK-UP:       evalf(Int(ln(z)^2/sqrt(1+z^2), z=0..infinity));

                Float(infinity)

The same problem with

                int(ln(z)^(2*k)/sqrt(1+z^2), z=0..infinity);

where k = 2, 3, 4, 5.

...............................................................................

BUG # 100 (int)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!  NONE Maple version can calculate this integral correctly  !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

******************************
***  SPURIOUS CONVERGENCE  ***
******************************

REPRODUCIBLE    ALWAYS

BUG HISTORY:    PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
                PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
                PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
                PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
                CANNOT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
                CANNOT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994

                int(Si(z)*ln(z), z=0..infinity);

ACTUAL:         1+gamma

EXPECTED:       infinity

CHECK-UP:       evalf(Int(Si(z)*ln(z), z=0..100));

                567.9000385

HINT:           plot(Si(z)*ln(z), z=0..100);

...............................................................................




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2002-2008 Cyber Tester Ltd. All rights reserved. All logos and trademarks are property of their respective owners.

E-mail: vb@cybertester.com