About average and operator

The matrix for angular momentum operators Lx, Ly, Lz are given.
Suppose a state with Lz=hbar (denotes h bar) , under this state find
out <Lx> and <Lx^2>

<Lx> = integrate (psi)* Lx psi dv
<Lx^2> = integrate (psi)* Lx^2 psi dv

However, the problem only tells us the state with Lz=hbar but we don't
know the close form of the state, how can we do the integration?
.

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