@Carl Love 

My point is that it is not very difficult to write a procedure with a local status for a variable.
 

@Carl Love 

Maybe something like this:

restart;
x:=10:
pl:=proc(f::uneval, r::uneval)
plot(f, r);
end:
pl(sin(x), x=-Pi..Pi);

@Carl Love 

I know, my answer was in the OP's context and it is correct.

@nm 

Because it is global.

@Carl Love 

Heinz'  is not that bad with a small change.

Heinz:= n-> min(select(d-> (d^2>n), Divisors(n))):

@Carl Love 

I wonder how useful is the type  `&+` due to the fact that the ordering of the terms in a sum could be difficult to predict.

@Al86 

This is not true. Take for instance p_0(t) = -t  or  p_0(t) = -t/2.
Not even when p_0 > 0.

@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.