If $a\sim b=a^2+b$ and $a\wedge b=b^2+a$, find $(3\sim 6)\wedge 2$.

First, let's unpack the internal function expression inside the parentheses:
$$3\sim 6=3^2+6=9+6=15$$

Now, evaluate the final function layer using $15\wedge 2$:

$$15\wedge 2=2^2+15=4+15=19$$