I'm working through some old qualifying exam problems and am wondering what I'm being asked to do in the following question: We have a random sample $\textbf{X} = (X_1, \dots, X_n)$ from a binomial$(m,\theta)$ distribution with prior distribution $\Theta \sim \text{Beta}(\alpha, \beta)$, where $m \in \mathbb{Z}^+, \alpha>0$, and $\beta>0$ are all known. Find the Bayes estimator for $\theta$ and $\theta^2$.
Here is where my confusion begins. Usually I am asked to find the Bayes estimator with respect to a loss function. There is no loss function given here. Hence, I am not sure how to proceed.
I have worked out that the posterior distribution is $\Theta | T \sim \text{Beta}(T + \alpha, \beta + nm - T)$ where $T$ is the sample sum.