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