Question: Where is the error coming from in this nested integration?

I have a pretty ugly nested integral (in my opinion) that I am trying to compute. I thought that I simplified the problem to an easier siutation however during my attempted calculations I am recieving: "Error, (in evalf/int) cannot handle unevaluated name `L` in evalhf

I am unsure where this is coming from, I would assume something in procedure or my attempted use of unapply is incorrect. Any comments are welcome, including those that state I am doing this entirely incorrectly. 


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