Graph of $(\lfloor(f(x))\rfloor)^2$

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How do I plot $(\lfloor x^2 \rfloor)^2$?

I know how to plot $\lfloor x^2 \rfloor$ from $x^2$. However, where do I begin with in plotting $(\lfloor x^2 \rfloor)^2$ from$\lfloor x^2 \rfloor$?

Or more generally, how do I plot $(\lfloor f(x) \rfloor)^2$?