Question: 14 hours for a numerical integration without any result

I'm running this numerical integration 14 hours continuously,without result.

The problem is the numerical integration

 evalf(int(F(q)*sin(q*Theta)/q)) assuming(0

This is taking forever.

Now,this is already done using Fortran (not time consuming at all),but the choice is not mandatory,so I'm using Maple 13.

Now,I think, to do this I have to do the integral using any other numerical method, evalf(int(,)) isn't good enough.

Now,the problem is- simpson or trapezoidal aren't suitable for improper integral.So help me out here.This is almost the last step of my calculations, if this can't me done all my calculations would be meaningless.

Here is an outline  of what I want to do, I want the result first,obviously it is a function of Theta.

Then I want to plot this for different values of Theta.Now I'm wondering how much time this plotting will take!

Theta is positive-real-number.

For F(q),see this WS 



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