non-linear scrolling

Scrolling s is like, well, linear:

s(x) = x             with x among [0, ∞]

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I'd like to apply a more fancy function, say x^2:

enter image description here

but I'd don't really know if it's possible and how...

I'd like to know your thougts on this.

EDIT

For example: is it possible to change the scrollTop value while scrolling?

Cheers.