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OOOHHH!! So I plug 999^4 into x in the equation!

You probably made a miscalculation for f'(a)=4(10^3)^3 with a ^3 too many.

The only time you use 999 is (999-1000).
You do not need 999 for f(a) nor f'(a), since a=1000.

Why do I use 999 instead of 999^4 at the end of the equation?

I think it's because 999 is x and f(x)=x^4, which is where the rest of my equations come from.

I put that in and the program counted it as wrong, make 999^4 just 999 and it counts it right.