Your worksheet contains quite a few syntax errors.  After fixing those, problems still remain.  For instance, σ is

Leter we want to integrate σ A with respect to z, where A depends on z as well.  Now, forget about the A for a moment.  How would you integrate σ by itself?  There is no antiderivtative in terms of elementary functions, so you wil need to do a numerical integration at best.  But then you will need numerical values for all the symbols.  But that's not possible either, since k and εα are the unknowns in your problem which need to be solved for.

A possible approach would be to define numeric values for all constants other than k and εα, then set up a Newton's iteration to solve the resulting system of two equations in two unknowns.  Such reformulation will take you far away from where you are now, so I don't think it's useful to speculate how that will work out.

@Met28 Your integral cannot be computed since it is divergent, as Alsholm has explained.

To appreciate the issue, see what you can do with the following simpler problem by hand, not by Maple:

int(1/(x-1), x=0..3);

You will find the exercise quite instructive.

This is not an answer to your question but a side note which you may want to take into consideration.

In your worksheet you have

    q := {q1(t), q2(t), q3(t), q4(t)};
    xm1 := q[1];
    xm2 := q[1] + l1 * cos(q[2]);

You have specified q as a set.  The order of the elements of the set is not necessarily predetermined, so there is no quarantee that q[1] will produce q1(t).  To fix the order of elements in q, give it as list rather than a set, as in

    q := [q1(t), q2(t), q3(t), q4(t)];

@acer What you are suggesting certainly makes sense.  Putting the orientation information in the PlotComponent should be no more demanding than putting it in Maple's toolbar, as it's done currently for some of 3D plots.  I hope to see that in a Maple in the near future.

Hello Acer, thanks for your very helpful response.  It solves my immediate problem.

I attempted to extend your examples by querying indets(G,'specfunc(:-ORIENTATION)') in order to get the plot's current orientation but it just returned the empty set.  I did "lprint(G)" to see G's contents but apparently there is no orientation information in it.  Is there some other trick to extract a 3D plot's orientation information?

I know that normally one can read the orientation angles theta, phi, and psi in Maple's toolbar.  Unfortunately that toolbar is not available when Maple displays an animation.

Rouben