The show didn't play on Broadway, so it might not count, but there's a VERY prominent robot in the musical version of Fritz Lang's Metropolis. The character spends most of the show in the form of Maria, but if the album is any indication, "Futura" should have had at least two scenes in the first act: the reveal of the Futura robot in the laboratory, and the Act I finale when Maria's likeness is transposed onto the machine.
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S.D.G.
(formerly "SweeneyPhanatic")