Huh, what are we talking about here? Calculus does give exact results. What questions are we talking about? Fundamentally statistical questions are going to have inherent uncertainties, its got nothing to do with Calculus.
Still not understanding what your issue is with calculus. I think so far you only have a problem with its outcomes when you feed it garbage. We expect to see "Calculus" diverge when integrating near the lattice spacing. I don't think we wholly disagree but I am doubtful you are going to make headway fighting against calculus.
I don’t have a problem with calculus, I’m just expressing its limitations. Using calculus to know the area of a circle is useful but it never really measures the area of a circle because the area of any circle is infinite.
What you are calling an exact result is only a limit function. All “things” will measure infinitely.