Late 50s -- invented by a guy named Jack Kilby at Texas Instruments. In the early 60's they already had hand-held caculators on the market.
No, no, no. Unless you were The Incredible Hulk.
If you don't believe me, consider this...
In the Apollo "command module" there was an "on board computer" that cost more than $20 million. Its operator display was big (like 8" by 12") and had several lines of big seven-segment numerals.
That computer had approximately the same processing power as the HP-65 programmable calculator that came out in about 1973, for $695. But the Apollo computer was designed in the mid-'60s, and was one of the reasons chips were invented (yes, I know there were others, but one thing at a time).
Believe me, if NASA could have put a hand-held calculator into Apollo, they would have.
In about 1966, Wang came out with a desktop calculator that was all-electronic. It could do square roots, IIRC. It had four little identical workstations that plugged into a central processor by means of thick cables. The central unit was about the size of a modern-day PC. They had "nixie tube" displays.
(steely)