The only problem was the brackets on the Integral functional, and the fact that it was in document mode made it much more inefficient.  Thanks you all for your suggestions.  I'm  a pretty new user to Maple, since this is a first-year undergraduate project and I've never really needed a CAS until now.  The algorithm works so I'm FINALLY over that hump (the sad thing is that I didn't notice the problem with the syntax for about 1.5 days of staring).

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The part I am working on is under "Etched".  Sorry for not resorting to attaching the entire file before, but I was not aware that I had the option. 

I just chose not to past the entire code because most of the code above this point is specific to the computation and doesn't affect the algorithm.  If you would like to see the rest, Ill paste it below:

Min := evalf(2*Pi*c/xMin);
Max := evalf(2*Pi*c/xMax);
i := 1;
while i <= 301 do
X := [op(X), evalf(2*Pi*c*L[i][1]/k)];
Y := [op(Y), L[i][2]*A*m*L[i][1]/(2*r*k)];
i := i+1;
end do;
plot(X, Y);

A, c, k, m and r are all constants and are compiled along with the other elements of the expression.  The only part that falters is the integral.

I just chose not to past the entire code because most of the code above this point is specific to the computation and doesn't affect the algorithm.  If you would like to see the rest, Ill paste it below:

Min := evalf(2*Pi*c/xMin);
Max := evalf(2*Pi*c/xMax);
i := 1;
while i <= 301 do
X := [op(X), evalf(2*Pi*c*L[i][1]/k)];
Y := [op(Y), L[i][2]*A*m*L[i][1]/(2*r*k)];
i := i+1;
end do;
plot(X, Y);

A, c, k, m and r are all constants and are compiled along with the other elements of the expression.  The only part that falters is the integral.