@Christian Wolinski 
Hi. I am trying to understand this procedure or function.
proc(E) global A; local S := proc(a, A) A, simplify(a) assuming A end; 'piecewise'(seq(S(E, a), a = A)); end(g(f(x)));

Also i get a warning

Warning, (in anonymous procedure) `a` is implicitly declared local

@jganding 
> f : = x->x^3:
> g : = x->x^(1/3):

>  f(g(-3))
>  -3

> simplify (g(f(-3))) assuming x>=0;

> 3/2 + 3*I*sqrt(3)/2

I also tried assuming x <= 0.

@nm  That trick won't work for x = -3.

>  f(g(-3))
>  -3

> simplify (g(f(-3))) assuming x>=0;

> 3/2 + 3*I*sqrt(3)/2

@nm  ( (-3)^3 )^1/3) =(-27)^(1/3) , shouldn't the latter equal to -3?
Hmm, i also notice 27^(1/3) does not simplify to 3. But 3^3 = 27.
This must have something to do with the cube root of 27 or -27, which has 3 values in the complex domain.
But then the surd function isnt much help either.

Thank you for all the responses. I am going over all the answers. Sorry I didnt respond sooner.

@John Fredsted 
I tried this code, it didn't work. I got
f := (x,y) -> x + y;
f([2,0],[3,4]);

output: [5, 4]

@Ronan He has a negative in his square root .

https://snipboard.io/CzjiFa.jpg https://snipboard.io/CzjiFa.jpg https://snipboard.io/CzjiFa.jpg https://snipboard.io/CzjiFa.jpg https://snipboard.io/CzjiFa.jpg https://snipboard.io/CzjiFa.jpg

@Carl Love 
I did post this question before.
https://www.mapleprimes.com/questions/230885-Maple-Help-Only-Works-Once-Per-Session

It was never answered satisfactorily, also if i try to repost it I get a warning
please don't duplicate. That means I have to delete the question?

@tomleslie 
Speaking of bugs and maple 2020... when I press F1 help multiple times, it stops working.
When use the maple command  ?<command>, it works only one time. Then won't open help again

I see the NULL command in one of your lines. I wonder what it does. This is an amazing code.

Specifically i would love to understand this line
C := coeffs(f(x, y), v, M); seq(`if`(member(op(i, [M]), N, 'j'), op(j, V) = op(i, [C]), NULL), i = 1 .. nops([M]));

@Joe Riel 

I am curious, why does 
" map(`+`, 3, L) "   output  "3 + [1,2,3]" ,  but  " map(`+`, L, 3) " outputs " [4,5,6] ".

On the other hand `*` displays commutativity in the arguments:
i.e.  "map(`*`, 3, L) "  and  " map(`*`, L,3) "  both output  " [3,6,9]"

@acer  I am using windows 10 pro, version 2004. Maple is release 2020.1

Below are some screenshots.

@dharr log10() is a useful command. Does not seem work with other bases, e.g. log2(8) .

@acer Sorry about that. Should I delete this post and repost a new one so that it appears on the right side where it says 'recent questions', or is this considered against etiquette.

@ecterrab Thanks for the file. It worked.