Numerical integration in python with variable limits

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I'm trying to numerically calculate the following integral:

The exact form of the functions doesn't matter.

I'm struggling with the innermost integral where the limits are variables of the outer integrals. I want to use sophisticated libraries like SciPy to do this, but its functions like quad, dblquad require numerical limits. Can someone help me with this?

I tried doing it manually by running for loops for every variable, but the precision is not great.

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