Evaluate integral with integrand-iterated boundary

Question

Related to something I read recently, I am wondering if there is some efficient way or popular method to evaluate the following definite integral that iterately takes as upper bound a modified version of its own integrand $$\int\limits_{0}^{\int\limits^{\int\limits^{\ldots} \sum\limits_{k=1}^{x-2}x^3B_{2k+3}}\sum\limits_{k=1}^{x-1}x^2B_{2k+2}}\frac{\sum\limits_{k=1}^{x}xB_{2k+1}}{\log\log\log \pi^x} dx$$ for $x < 100$. I did not found something within the search quickly but I am curious since this kind of integral looks interesting, especially together with the Bernoulli numbers.