@alljoyland 

It would help if you could post a link to a picture of some mathematical text which has the features that you are trying to describe. Even a picture of some handwritten mathematical text would help.

@alljoyland 

No, your expression

sum(a[i[m]]*diff(f[m](x),x), i= 1..4)

is not "okay" or "natural" if you iterate over i. It would be okay if you iterate over m:

sum(a[i[m]]*diff(f[m](x),x), m= 1..4).

You should've mentioned that the combstruct package is a part of regular Maple. It does not need to downloaded separately.

@Axel Vogt Please post the steps to convert the integral to [0..1]^4.

@acer Thanks, that's really deep sleuthing, man. I suspected that the difference was in assigned but I couldn't see that code.

Could you please provide the source of the Maple code, its date of publication or posting, and a rough translation into mathematical English of any surrounding text?

What is your suggested value for "Zeigerlange vom Punkt (0,0) bis Pk in mm"?

The first problem is that there are some weird characters in the code and some inappropriate usage of unevaluation quotes (as in EE_:= 'E_ - P0_';). But even after correcting those I get errors.

@Thomas Richard The Cuba methods and all of Maple's numerical multiple integration methods are limited to regions of integration that are hyperrectangles. Perhaps there is a way to convert this integral thus.

@Axel Vogt 

What is the essential difference between

int(..., numeric, epsilon= ...)

and

evalf(Int(..., epsilon= ...))?

Your Question has two attached worksheets with the same name. Are they in fact the same worksheet? Your cover text implies otherwise. If they are different, they should have different names.

@Mac Dude Thank you for selecting my Answer.

When I use unevaluation quotes, I try to keep the "span" of the quotes as narrow as will get the job done, even if that means I need some extra pairs. So, I did ''Vector''('Element') rather than ''Vector(Element)''. This helps me---a tiny bit---to understand which parts are being evaluated and when. Still, figuring out when multiple pairs of quotes will be needed is my least-understood part of the Maple kernel (from my user-level grey-box perspective---I have no direct knowledge of the kernel code).

I am still baffled by this difference between Maple versions. See the recent comments to Acer's Answer below.

@acer I've looked through the code for TypeTools:-Exists, its needlessly opaque underling TypeTools:-known, and TypeTools:-AddType in both Maple 16 and 18. I can see no change. Do you have any conjecture about the reason for the difference? Are you aware of any kernel-level change in evaluation rules?

@acer Can you confirm whether the two pairs or quotes do make a difference in Maple 17 or Maple 16.02 (which I used)?

@Athar Kharal Using Maple 16.02, I get no square brackets.

@sazroberson 

Most of StringTools is that way, and they are also not thread safe.

@sazroberson 

Your technique of initializing the list will only work for lists with fewer than 101 elements. Maple begrudgingly allows this extremely inefficient technique for these short lists. Every time an assignment is made to the list, a new list is created, and all the other elements are copied to the new list. That's what I meant by the interpretter faking it to make it look like a list is being modified.

I see no point in learning these techniques.