Depending on what you mean by that, a "completely even set of points" on the sphere may not be possible.  For N points with a statistically uniform distribution on the sphere in R^n, try something like this.

> with(Statistics):
  Z:= RandomVariable(Normal(0,1));
  L:= Sample(Z, N*n);
  R:= [seq(add(L[i]^2,i=j*n+1 .. (j+1)*n)^(1/2),j = 0 .. N-1)]; 
  A:= <seq(L[j*n+1 .. (j+1)*n]/R[j+1], j=0..N-1)>;

The points are the rows of the resulting Matrix A.

> select(t -> degree(t,{x,y,z})<=8, expr);

> select(t -> degree(t,{x,y,z})<=8, expr);

Do you mean like this?

> Matrix([seq(readdata(cat("/Users/humadih/test/",i,".tmp"), 1), i = 1740 .. 1770)]);

Do you mean like this?

> Matrix([seq(readdata(cat("/Users/humadih/test/",i,".tmp"), 1), i = 1740 .. 1770)]);

First thing to note: the change of variable t = sqrt(mu)*s makes this into

Int(mu^(1/2)*s^2*exp(-1/4*(s^4+delta^2)/s^2)/(s^2+delta),s = 0 .. infinity)

so the answer is sqrt(mu)*J(delta) where J(delta) = Int(s^2*exp(-1/4*(s^4+delta^2)/s^2)/(s^2+delta),s = 0 .. infinity).

I don't know if this integral has a closed form.  Might a series expansion in delta be useful?

First thing to note: the change of variable t = sqrt(mu)*s makes this into

Int(mu^(1/2)*s^2*exp(-1/4*(s^4+delta^2)/s^2)/(s^2+delta),s = 0 .. infinity)

so the answer is sqrt(mu)*J(delta) where J(delta) = Int(s^2*exp(-1/4*(s^4+delta^2)/s^2)/(s^2+delta),s = 0 .. infinity).

I don't know if this integral has a closed form.  Might a series expansion in delta be useful?

Even in Document mode, assignments get fully echoed if Typesetting Level is set to Extended.  I don't know the logic (if any) behind this.

 Also in Extended typesetting, you can "Allow shortcut function definition" to Never or Always as well as the default Query.

A look at the graph (with implicitplot) suggests that it may be better to express this in terms of x+y and x-y. 

> eq:=cos(x+y)*sin(x-y)=cos(x)^2-sin(y)^2:
  _EnvAllSolutions:= true;
  solve(eval(eq,{x=s+t,y=s-t}));

{s = 1/4*Pi+2*Pi*_Z4, t = t}, {s = -3/4*Pi+2*Pi*_Z4, t = t}, {s = s, t = 1/8*Pi+Pi*_Z3}, {s = s, t = -3/8*Pi+Pi*_Z3}

> map(subs,[%],[x=s+t,y=s-t]);

[[x = 1/4*Pi+2*Pi*_Z4+t, y = 1/4*Pi+2*Pi*_Z4-t], [x = -3/4*Pi+2*Pi*_Z4+t, y = -3/4*Pi+2*Pi*_Z4-t], [x = s+1/8*Pi+Pi*_Z3, y = s-1/8*Pi-Pi*_Z3], [x = s-3/8*Pi+Pi*_Z3, y = s+3/8*Pi-Pi*_Z3]]

So far I see one discussion: www.linkedin.com/groupAnswers

and "news" links to articles in Design World News, Konstruktionpraxis, (apparently the German version of the previous article) and Desktop Engineering.  Not a lot, but not quite "nothing".

That code imports a file "energy scan annealed and etched.xls", which of course we don't have.

But one error jumps out at me: you have Fmod := 2/Pi*int[...] instead of int(...).  Could that be the source of your problem?

Debugging code such as this would be  a lot easier if you used 1D Maple input instead of 2D Math, and Worksheet Mode with separate input regions instead of Document Mode with everything in one. 

That code imports a file "energy scan annealed and etched.xls", which of course we don't have.

But one error jumps out at me: you have Fmod := 2/Pi*int[...] instead of int(...).  Could that be the source of your problem?

Debugging code such as this would be  a lot easier if you used 1D Maple input instead of 2D Math, and Worksheet Mode with separate input regions instead of Document Mode with everything in one. 

myMatrix:= <<1,2>|<3,4>>;
with(Maplets[Elements]):
maplet := Maplet(FileDialog['FD1'](
    'title'="Save As",
    'filefilter' = "txt",
    'directory' = currentdir(),
    'filterdescription' = "Text Files",
    'approvecaption'="Save",
   'onapprove' = Shutdown(['FD1']),
   'oncancel' = Shutdown()
)):
R:= Maplets[Display](maplet):
if R = NULL then error "Save Cancelled"
else
  S:= op(1,R);
  if not StringTools[Has](S, ".") then S:= cat(S,".txt") end if;
  save(myMatrix, S);
  printf("Saved to file %s\n",S);
end if:

myMatrix:= <<1,2>|<3,4>>;
with(Maplets[Elements]):
maplet := Maplet(FileDialog['FD1'](
    'title'="Save As",
    'filefilter' = "txt",
    'directory' = currentdir(),
    'filterdescription' = "Text Files",
    'approvecaption'="Save",
   'onapprove' = Shutdown(['FD1']),
   'oncancel' = Shutdown()
)):
R:= Maplets[Display](maplet):
if R = NULL then error "Save Cancelled"
else
  S:= op(1,R);
  if not StringTools[Has](S, ".") then S:= cat(S,".txt") end if;
  save(myMatrix, S);
  printf("Saved to file %s\n",S);
end if:

In general, consider a DE diff(y(r),r,r) = - b * diff(y(r),r)/r + f(y(r)) where b > 0. 

Note that diff(y(r),r,r) + b*diff(y(r),r)/r = r^(-b) * diff(r^b * diff(y(r),r), r).  If there is a constant A such that  f(y(r)) < A for sufficiently large r, then for such r we have

diff(r^b*diff(y(r),r), r) < A*r^b

, so for some constants C1 and C2,

y(r) < A*r^2/(2*(b+1)) - C1*r^(1-b)/(1-b) + C2 [ in the case b=1, replace the r^(1-b)/(1-b) by ln(r) ], and similarly if the inequalities are reversed.  In particular, the only way for y(r) to have a finite limit L as r -> infinity with f continuous at L would be to have f(L) = 0.