It appears as though the newer code uses an approximation to Rademacher's series for the partition function. To "fix" it, I modified the exit condition:

numbpart := subs(0.1=0.03, eval(combinat[numbpart])):

With that change, the results for the given values agree with the expected values.

length(N);
                       400

The meaning of length depends on the type of input. For positive integers it is the number of digits.

I'd be surprised if you had copyright, considering, if I understand correctly, that you didn't compose the original and used an online translator.

The range for y should be y = a .. 3*a.

The range for y should be y = a .. 3*a.

The specific counterexample

f := x*y*(x^2-y^2)/(x^2+y^2);

is well defined everywhere except at the origin. 

f_xy := diff(f,x,y):

This fails to evaluate at the origin:

eval(f_xy, [x=0,y=0]);
Error, numeric exception: division by zero

However, if we separately evaluate x=0 and y=0 we do get the expected limits:

foldl(eval,f_xy,x=0,y=0);
                                         -1
foldl(eval,f_xy,y=0,x=0);
                                          1

Better to substitute a parameterized line in a particular direction ...

f_xy_00 := simplify(eval(f_xy, [x=t*cos(phi),y=t*sin(phi)]));
                                  6              4             2
           f_xy_00 := -16 cos(phi)  + 24 cos(phi)  - 6 cos(phi)  - 1

Do you have an example in mind?  With appropriate technique one can readily evaluate, with Maple, the counterexample to Clauraut's theorem given in Wikipedia.

Did you execute the command

with(VectorCalculus);

For the diff-eq, use diff(y(x),x) and diff(y(x),x,x) to represent the first and second derivatives of y with respect to x and pass the equation to dolve.  You can also use 2D input with the prime notation, provided that View -> Typesetting is configured so that y' translates to diff(y(x),x), etc.  Here I'll use alias:

alias(y=y(x)):
deq := diff(y,x,x)-2*diff(y,x)+2*y=4*exp(x)*sin(x):
dsolve(deq);

You can provide initial conditions to solve for the integration constants.
 

Did you execute the command

with(VectorCalculus);

For the diff-eq, use diff(y(x),x) and diff(y(x),x,x) to represent the first and second derivatives of y with respect to x and pass the equation to dolve.  You can also use 2D input with the prime notation, provided that View -> Typesetting is configured so that y' translates to diff(y(x),x), etc.  Here I'll use alias:

alias(y=y(x)):
deq := diff(y,x,x)-2*diff(y,x)+2*y=4*exp(x)*sin(x):
dsolve(deq);

You can provide initial conditions to solve for the integration constants.
 

Consider the area bounded by the x-axis and [x,y] = [t,t^2+1], t = -1..1.  It is y-axis-convex but not x-axis convex.  At least that is my understanding.  As an example of something that is both x and y axis-convex but not convex, consider an elbow:

+--------+
|        |
|  +-----+
|  |
|  |
+--+

Here's link to books.google.com/books that concludes the excerpt I previously posted: "We say that L is axis-convex if each line parallel to its axis that meets it does so in a (possibly degenerate) line segment."

Last night I searched Google for a definition.  There were a couple uses, but no clear definitions.  This thumbnail, or what I can glean from it, seems similar to your, "L is said to be axis-convex if each line parallel to its axis which ....; however, the author uses "axis" to indicate an axis of symmetry of the object and not the coordinate axes. The rest, alas, http://www.jstor.org/pss/2154703, requires a subscription to JSTOR.

Alex,
I think there is a missing negation in your response (below): "... it appears that the student does [not] distinguish ...". You should still be able to edit it, since there are no replies (yet) to it.  I tried to send you a private mail, but MaplePrimes said that you don't exist, which seems unlikely.

Alex,
I think there is a missing negation in your response (below): "... it appears that the student does [not] distinguish ...". You should still be able to edit it, since there are no replies (yet) to it.  I tried to send you a private mail, but MaplePrimes said that you don't exist, which seems unlikely.

Your plot example is a red-herring.  Neither can Maple handle

plot(t^2, t=0..T);

because plot requires numeric endpoints.  If Maple ever implements symbolic plots (hah) then plot(f(t), t=0..t) should (ideally) be valid.

I'm not sure what weakness you are referring.  int(f(t), t = g(t)..h(t)) should be (and is) allowable, despite the limitations of some calculus instructors.

Your plot example is a red-herring.  Neither can Maple handle

plot(t^2, t=0..T);

because plot requires numeric endpoints.  If Maple ever implements symbolic plots (hah) then plot(f(t), t=0..t) should (ideally) be valid.

I'm not sure what weakness you are referring.  int(f(t), t = g(t)..h(t)) should be (and is) allowable, despite the limitations of some calculus instructors.