This 'diffop2de' command is what I was looking for, thanks! 

@tomleslie Thank you for the detailed answer! I was not aware of the add() command and it seems a good idea in such a case! I have not been able to get the analytical form of the integral with Maple. Hence will try the add(evalf(Int( ))). Also, would you suggest specifying the _d01ajc method even if my integrand is smooth and has no singularity on the domain of integration? Finally, you suggest specifying local variables for summation indices could decrease the computation time? (That makes sense since to me!) Thanks a lot for the code snippet on the bonus question. Will try and comment the results!

@acer Okay, I thought there would be an approach that is specifically better; thank you for pointing that out. About the integrand, Maple have not been able to analitycally perform any of the integrals I deal with. Will definitely check for the add command and specifying methods since indeed my integrand has no discontinuities. Thanks!

Unfortunately, the integrand really is messy (and long and defined in terms of many previously defined functions) and I'd rather not include it here. Plus I am trying to perform this on different integrands. But may I ask in general: if you want an numerical evaluation, where do you use "evalf()"? Are nested use of the evalf() command a good idea? For example is going evalf(Sum( evalf(Int( ))) a good idea, or there is redundancy in the evaluation that will ultimately slow down the computation? - So simply going with evalf(Sum( Int( ))) would be best. What about sum(), int(), evalfh(): could these help in this "nested" scenario?

Here I really am trying to optimize on time rather than on accuracy. Will look into the options you mentioned!

Thank you for your answer!

@gkokovidis Thank you! It works now!