@Al86 

It is not possible to maximize an expression depending on an unknown function (p_0 in this case).
It's just like asking for max { f(t): t in [0,1] } with no information about f().

Or, is the problem a variational one?

@Adam Ledger 

Your function F computes the set {p^t :  p is a prime, t is a power of 2, p^t | n} \ {2}.
This can be done much more efficiently using ifactors(n).

F:= n -> {seq(seq(p[1]^(2^j), j=0..ilog2(p[2])), p=ifactors(n)[2])} minus {2}:

@Markiyan Hirnyk 

I think that I have explained the problem crearly in my reply.
Note also that MultiSeries:-asympt(f,n,3) assuming x>0;  is even wronger.

@Markiyan Hirnyk 

Have you read my reply, or your "does not correspond to reality" was automatic?
a contains the asymptotic for real n --> oo. It is wrong. Please note that this result is used even when n::posint, so we cannot consider it as being correct in this case.

@Markiyan Hirnyk 

Thank you.
Unfortunately the asymptotic expansion obtained by Maple is wrong!

Download asympt.mw

@Adam Ledger 

From the user's point of view, it doesn't matter whether a procedure is in the kernel or in the library (except the speed and the posibility of being traced/viewed). It's the designer's decision; it is not unusual for a procedure to be moved from the kernel into the library or viceversa.

@Carl Love 

You are right. I can't explain why I did not use it.

@acer 

I also think that the "methods" associated to such objects should be better documented (with examples) for a user who is not necessarily interested in working with objects. It seems that all the new packages are implemented with objects; this is of course more flexible but the user will have problems to understand how exactly they work and what are the side effects.

@Carl Love 

sqrt(1+x^2)  is almost flat (≈ x) and the sine is nicer :-)

@Mariusz Iwaniuk

plot([f(x), 'fdiff(f(t), t = x)'], x = 0 .. 10);

@torabi 

Your ode seems to have some kind of logarithmic singularity at r=0.

For example:

a:=3.; b:=20.;
BCab:=
{ u(R0) = UB,
  D(u)(R0)= a,
  ((D@@2)(u))(R0) = -a/R0,
  ((D@@3)(u))(R0) = b
};
sola:=dsolve({f1, BCab[]}, numeric):
plots:-odeplot(sola, [r,u(r)], r=1e-15 ..1);

The problem is whether for some a,b  this singularity vanishes.

I think that you should try to study theoretically the problem (using e.g. some asymptotics, a change of variable etc) because numerically it will be probably difficult or unreliable.

@mmcdara 
The string approach is not "optimal" because  567 will be converted to 5b7 (nonsense).

 sqrt(b)/b = 1/sqrt(b)  is valid  for any complex (nonzero) b.

@Joe Riel 

But for a:=sqrt(6)/6 + sin(5/6) + exp(6/7);  more work is needed

You do not have a parallelipiped; you have two planes P1 and P2. If they were parallel, it would be possible to compute the distance between them. But P1, P2 are not parallel, so it's not clear what is the question.

@AliahNiu 

You can use Maple to check if an integral exists (i.e is finite in your case, being >0)  if you give numeric values
for parameters (a,b,p,d). Then use int(...)  or int(..., numeric).