Do you have more than 4 cores? I think Windows maybe having some sort of limitations in this respect. Check it.

@Stretto Your code should be:

E := proc(f, x, depth)
   if depth = 0 then x else
# Trying to actually compute f(f(x)), say. I know we can just loop.
      E(f, f(x), depth-1);
#or
#      E(f, f[depth](x), depth-1);
  fi;
end proc:

as only the innermost f takes x as argument.
Looped version:

E := proc(f, x, depth)
   local i, coord:=x;
   for i from depth to 1 by -1 do coord:=f(coord) od;
#or
#  for i from depth to 1 by -1 do coord:=f[i](coord) od;
end;

@alexk213 .167084168057542165456902860033807362201524292515164404031254374190731323852253210417020805425

Maple 2017 agrees with your second value (python) at Digits:=15; and with the first one at Digits:=11;.

@AhmedRahby Are you trying to change variable ordering?

@Carl Love That sounds confused. Clarification:

D[1, 2](1/x)(s, t) means diff(1/x(s,t), s, t). D[1,2] means first derivative in first coordinate, first derivative in second coordinate. Your expression D[1, 2](1/x); implies x is a function of 2 coordinates.

@Carl Love Edit:
Observing Maple 5.4 I asserted you were correct. This was already implemented in Maple. Here is a demonstration for Maple 5.4 (it does not work in Maple 2017):

restart;
constants := constants, '_EnvConstants'; 
S := {x^2 + y^2 - 1};

proc() 
_EnvConstants := x;
solve(S);
end(); 

proc() 
_EnvConstants := y;
solve(S);
end();

proc()
_EnvConstants := NULL;
solve(S);
end();

Above code does not give desired output in Maple 2017. Here is a poor improvisation:

restart;
_EnvConstants:=:-constants;
 
S := {x^2 + y^2 - 1};

proc() 
:-constants:=_EnvConstants, x;
solve(S);
end(); 
:-constants:=_EnvConstants:

proc() 
:-constants:=_EnvConstants, y;
solve(S);
end(); 
:-constants:=_EnvConstants:

proc() 
:-constants:=_EnvConstants;
solve(S);
end(); 
:-constants:=_EnvConstants:

@Carl Love Constants are not treated as variables by solvers. One way to consider different interpretations of a problem is to redeclare constants. It is a sensitive task. An envvar is precisely intended to deal with this situation. Within the scope of a procedure anything can be done with it. Let us consider an envvar that extends the global constants, so that constants are those found in: constants, EnvConstants.

@acer I think you are misinformed. I made a followup response in that question thread and I then made a post with the same statement I used. Someone has deleted that post and modified the question thread into a post (to take place of the one I created). When I saw this doubt arose in me, for if I change the post back into a question it may be changed yet again. I voided this problem by deleting the whole thing. I reserve "posts" for presentations/factual data and "questions" for queries.

Do we know who was acting here?

@Christopher2222 Well after I reposted someone deleted it again. I dont care this much to put up with this.

@Christopher2222 I think I still have a copy&paste of it. I'll repost today.

Someone deleted my post and then converted my question into a post to replace it. I deleted the new post. My apologies.

@Rouben Rostamian  You wish for what once was, as do I. Maple 5.4 had an arbitrary amount of sources of light. I never checked limits for it. I imagine their new interface coerced this change. Lame.

@Carl Love I just found this online, quite randomly since I gave up on this issue.

From Maple Help page:

I tried again with Maple 5.4 and Maple 2017. Result is clear: Maple 2017 render is bugged.
Some observations:
1) only the last light in the sequence of lights is applied to the object
2) the condition persists when using DAG objects.

L:=[[(45.0, 45.0, 0.0, 0.0, 0.9)],[(45.0, 45.0, 0.0, 0.9, 0.0)], [(135.0, 0.0, 0.9, 0.0, 0.0)]];
plot3d(1, alpha = 0 .. 2*Pi, beta = 0 .. Pi, coords = spherical, color = white, style = patchnogrid, view = [(-2 .. 2)$3], axes = boxed, scaling=constrained, grid=[81,41], light=L[1], light=L[2], light=L[3],ambientlight=[0.5,0.5,0.5]);
plot3d(1, alpha = 0 .. 2*Pi, beta = 0 .. Pi, coords = spherical, color = white, style = patchnogrid, view = [(-2 .. 2)$3], axes = boxed, scaling=constrained, grid=[81,41], lightmodel=light3);

Maple 5.4:

Maple 2017:

@Carl Love So that is the difference. They removed colors from light models. How pathetic.