Let
\[f(x) = \begin{cases} |\lfloor{x}\rfloor| &\text{if }x\text{ is rational}, \\ \lceil{x}\rceil^2 &\text{if }x\text{ is irrational}. \end{cases} \]
Find $f(\sqrt[3]{-8})+f(-\pi)+f(\sqrt{50})+f\left(\frac{9}{2}\right)$
\(\begin{align*} f(\sqrt[3]{-8})&=|\lfloor{-2}\rfloor|=2\\ f(-\pi)&=\lceil{-\pi}\rceil^2=-3^2=9\\ f(\sqrt{50})&=\lceil{\sqrt{50}}\rceil^2=8^2=64\\ f\left(\frac{9}{2}\right)&=|\lfloor{\frac{9}{2}}\rfloor|=4\\ 2+9+64+4&=\boxed{79}\\ \end{align*} \)
+230 
