Let $$e$$ be the base of natural logarithm and let $$f : \{1, 2, 3, 4\} \to \{1, e, e^2, e^3\}$$ and $$g : \{1, e, e^2, e^3\} \to \left\{1,\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$$ be two bijective functions such that $$f$$ is strictly decreasing and $$g$$ is strictly increasing. If $$\phi(x) = \left[f^{-1}\left\{g^{-1}\left(\frac{1}{2}\right)\right\}\right]^x$$, then the area of the region R = {(x, y): $$x^2 \leq y \leq \phi(x)$$, $$0 \leq x \leq 1$$} is: