Let f be a differentiable function defined on [0, (π)/2] such that f(x)>0 and f(x)+∫_0^x f(t) √(1-( log_e f(t))^2) d t=e, ∀ x ∈[0, (π)/2]. Then (6…

Let $\displaystyle f$ be $\displaystyle a$ differentiable function defined on $\displaystyle \left[0, \frac{\pi}{2}\right]$ such that $\displaystyle f(x)>0$ and $\displaystyle f(x)+\int_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$. Then $\displaystyle \left(6 \log _e f\left(\frac{\pi}{6}\right)\right)^2$ is equal to $\displaystyle \_\_\_\_$.