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"in 1974 I experienced an invasion of my mind by a transcendentally rational mind, as if I had been insane all my life and suddenly I had become sane."
- Philip K. Dick

Grantline Comptometer  
  Key-driven computer/calculator that easily solves even calculus problems.  

The Grantline Comptometer is a very early reference to computers or machines that can solve even the most complex problems simply by entering the necessary parameters of the problem.

Above it was a shelf, with one of the Grantline comptometers, the mathematical sensation of some years back. It was almost a human mathematical brain.

Under its keys the most intricate problem of calculus was automatically resolved, as surely as an ancient adding machine did simple arithmatic.

From Beyond the Stars, by Ray Cummings.
Published by Ace in 1928
Additional resources -

This device was an extension of the Felt Comptometer, a calculating machine that was first built in the 1890's and developed through the 1930's. Comptometer schools were opened, and equipped with the machines to train the necessary operators. Comptometers had full rows for sets of numbers; it didn't matter what order the digits were entered. Early versions performed addition and subtraction; later models performed multiplication and division, and even square roots.

The Grantline Comptometer presages systems like Mathematica, that actually do allow the user to type in a calculus formula; the software then solves the equation for you.

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