Mathematica pseudo-types Integer, Real, Rational, Complex, String and Symbol, and their use.

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Compilation error: “Could not complete external evaluation at…”

I'm pretty new to trying to use Compile[], and I just can't see why I'm getting this error. I have two functions to define beforehand; one of them is a bit odd: ...
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Pattern type and list indexing warnings/errors

I'm new to Mathematica and am trying to implement some simple noise functions in it in hopes of eventually finding an integral for them. This is the interesting part of the code: ...