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Using InterpolatingFunction from NDSolve

I solved a PDE with NDSolve in Mathematica 5.1. I could plot,
differentiate and integrate the obtained InterpolatingFunction object,
the result being a similar object. I was able to integrate the 2nd
derivative of it. What I need is to integrate the square of the
obtained InterpolatingFunction object (the square itself does not
simplify to such an object).
You can see the details on my homepage:

Every suggestions are welcome!

Thank you,

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