[uuDevil]

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HP32SII: 37,000,037

Edit: Also, TI89: 37,000,023.310015

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37,000,037 is what you would get if did the 1 - first, and then replace the ^ with *. So you would have 1 / (1/1000001 * 1/37).

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I'm a little rusty w/ RPN, but the key sequence

1000000[ENTER]1000001[DIVIDE]37[1/x][y^x][+/-]1[+][1/x]

gives a result of 37000037 on my HP 32SII.