Re: Extended PEMDAS.
You may wish to check these out:
This is a really good intro on parsing. I know people suggest using external libraries, but I'd implement one myself first to see how it all works. You'll learn much more doing so.
The next two chapters also may give insights into how to structure your expressions. They build an AST (Abstract Syntax Tree), which is what the examples in post 3 are, just without the fancy class representations. Obviously you have a much simpler goal -- constructing a basic calculator -- but all you'd have to do is reduce the tokens you scan for.
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