@Rouben Rostamian Many thanks for your response. This has been most helpful.
You are absolutely right, though. The approximation does not even come close to providing the precision I'd need for an instructive evaluation of my integral.
In a nutshell, I am trying to implement an iterative procedure. I attached a quick worksheet with the first 5 iterations: Example.mw. (I am sure that this is written in a horribly inelegant manner. My apologies.)
My eventual goal is to write a loop that would enable me to recover the, say, 100th iteration of the function h. Unfortunately, however, I found that my Laptop fails to go anywhere beyond the 5th iteration. When I do the integration "myself", in that I partition the integration range, copy and paste the relevant expressions, and add the resulting integrals, I am able to come up to the 11th iteration.
It seems to me that I am not even trying to do anything computationally expensive. I just don't know how to use Maple in order to tackle my problem in a somewhat more efficient way.
Thank you so much.