Create a calculator powered by human power. Set up a computation, perhaps mechanically, then turn the crank. How sophisticated a calculation can it do, and how many turns of the crank will it need? Probably done by having the crank power an electric generator which powers an electronic computer, though it'll take some engineering for the computer to be able to work on the "dirty" power generated from a crank. Booting up an operating system at the start of a computation is a no go.
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