@C_R I just corrected the link

@C_R The above fmod may be not quite what one wants since fmod(10,10) returns 10.0 instead of 0.

For positive numbers frac(t/m)*m already works, more general use R:= (t,m) -> t - floor(t/m)*m,
see https://www.mapleprimes.com/questions/36061-Modulo-Not-Only-For-Integers#answer60554 (Robert Israel)

Your expesssion is (-csgn(sqrt(-1 - sqrt(3)*I)*(8*x^(3/2) + c)^(1/3)) - 1)*sqrt(x), c__1=c/12

Why not using the File Explorer ?

I do not expect that Maple covers everything in teaching.

For your last examples I would consider limits and continuity of products or squaring or similar to interchange operations, say f(x)*g(x) for f(x)=x, g(x)=x*ln(x) or lim(h(x)^2) = lim(h(x))^2 for continuous functions.

Enough from my side for this thread.

You might have a look at Wikipedia and its explanations, https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

There is no need to understand Mathematics by using Maple

For my very old office PC I get roughly 1/2 minute, 15 times slower than dharr. Not that bad (Maple 2024.1, Win 7, Intel Pentium 630, 2.70 GHz, 2 CPUs)

@nm Current versions do not treat *.mws as classical sheet

I saved your sheet *.wm as classical sheet *.mws - then print(e) in Maple 2017 has not problems

I downloaded the file Maple2024.1WindowsX64Upgrade.exe which is ~ 300 MB and thus can not be a complete version which is more than 3 GB

For your purpose I guess you will need 2 installations of Maple 2024 and will upgrade 1 of these

@dharr 

A good working horse is double exponential integration with oscillating factor to integrate g(r)*sin(a*r + b) over the half line 0 <= r. Unfortunately Maple does not have it but I once translated code for it, https://www.mapleprimes.com/questions/128564-Any-Way-To-Reclaim-NAG-d01akc-Allocated.

Also note that Wminus and Wplus differ only by 2*m*x, so those integral need not be computed twice

PS: the originator writes (in his post) that he can not reply ... strange, I would just create a new account

@dharr The poster seems to consider the expressions as functions of x (without saying something about the range for x). With increasing x the task leads to highly oscillating integrals and Maple is weak on that. Already with Digits=15 and x=0.001 (or Digits=10 and x=1.0) that direct approach does not work. Likewise you may try to estimate the magnitude of the integral to see that it does not contribute to the numerical result

Remark and first suggestion:

You may try to provide the definitions of your function and constants using MMA syntax (as text). In most cases it can be turned into Maple expression using "convert(..., FromMma). This would avoid typing it again. But probably nobody will do the typing for you.

may be it hangs in one of the methods

Maple 2017 finds it