Lambda as a source of energy

This week, CQW has a guest question by U. Bastian: is it possible to tap dark energy as a source of (mechanical) energy? could you set up a machine that would accomplish this?

bonus question: Assume you’re trying to compute the expectation value \(\langle x\rangle\) of a random distribution \(p(x)\mathrm{d}x\), which has the cumulative distribution \(P(x)\). you could write: \(\langle x\rangle = \int\mathrm{d}x\:xp(x) = \int\mathrm{d}x\:x\frac{\mathrm{d}}{\mathrm{d}x}P(x) = xP(x) - \int\mathrm{d}x\: P(x)\) by integration by parts, where all integration boundaries are taken to be \(-\infty\ldots+\infty\). Both expressions in the final expression are not finite. Where’s the mistake?