@peter2108 
You already have writebytes for this.

@ecterrab 

I just want to note that in the first integral (J), the change of variables was not done at all. J was simply rewritten using intat.

@Rouben Rostamian  

The EPS export for 3D is (and was) totally wrong (at least in Windows 64 bit).
plot3d(x^2+y^2, x=-1..1,y=-1..1);
(I have posted twice the result in the past.)

@tomleslie 
The same version and OS.

The worksheet executes correctly for me.

@Christian Wolinski

collect(evala(Norm((lhs-rhs)(A))),Y,`convert/parfrac`);

@Carl Love 
Yes, I have corrected.

@Carl Love 

No, I din not think much about it. But it seems that a more general fact is true.
If p is a fixed prime and 2 <= k <= p-2 is also fixed then the events
A = {a in {1,...,p-1} :  a is prime} and
B = {a in {1,...,p-1} : a^k mod p  is prime}
are "asymptotically independent". For k=p-2 one obtains the inverses mod p.

@Carl Love 

Actually the two events are not independent (for a fixed p). They seem to have some kind of "asymptotic independence" (p --> oo).
It's interesting your intuition about this!

@acer 

It could be that the integral is exactly 1/8 but I have not time now to check.

@digerdiga 

The numerical integration is easier for rectangular domains and it is always possible to reduce the integral to such domains via a change of variables.
Note that we may include the domain D in a larger rectangle R and define the function 0 in R \ D but this is not the best solution because the new function is (generally) not continuous.

@brian bovril 

This version of alphametics is much faster and uses an intelligent algorithm (not the brute force one). It works even for systems of "equations".
The author is Robert Israel.

@Gabriel samaila 

I see that you have chosen infinity = 1. If you choose a larger value the results are closer.
But I am a mathematician, not an engineer; you will have to fine tune it yourself; for a too large value dsolve may fail or must also be fine-tuned (there are many options for this).

@baharm31 

It works for me. After all it's a linear ode system with constant coefficients which is well known to Maple.

2DOFnumerical-x.mw

@Gabriel samaila 

You must also insert a * (or a space) after M as Rouben noticed. Note that in Maple  7(x) simplifies to 7, not to 7*x.