If $F(a, b, c, d) = a^b + c \times d$, what is the value of $x$ such that $F(2, x, 4, 11) = 300$?
Plugging in, we have that $2^x + 4\times 11 = 300$.  This rearranges to $2^x = 256$, or $x = \boxed{8}$.