Conjugate prior posterior mean

Let $X_1,\dots ,X_{10}$ be a random sample from a distribution with the probability density function f(x|$\theta )=\theta x^{(}\theta -1)$ if 0 < x < 1, and 0 otherwise, where $\theta >0$ is an unknown parameter. The prior distribution of $\theta$ is given by $\pi (\theta )=\theta e^{(}-\theta )$ if $\theta >0$, and 0 otherwise. The Bayes estimator of $\theta$ under squared error loss is