I bought an Elektronika МК-61 Soviet-era RPN calculator on eBay from sovpedia.
Repair
It didn't work when it arrived, so I rooted around and got a schematic from Alfred Klomp in Holland, who has an excellent page in English on hacking the MK-61. (There's also a schematic on Wikipedia but it's a little hard to read; back versions of it are larger.)
At first, the whole assembly pulled no current, so I looked for an open, and found it: the AC adapter jack has a shorting connector which was either corroded or mechanically unstable. I cleaned and adjusted the shorting bar with a small screwdriver.
Keys
Most of the keys are easy to figure out, but it's interesting that the ENTER key doesn't have a special size or location; it's labeled B-uparrow (perhaps вводить). Greg Riscov has an explanation of the MK series keyboards. (mirror zip in case tripod goes the way of geocities.)
Schematic
Quick Reference Card
I've also produced a quick reference card based on the above pictures and descriptions from Gregory Escov and Andrew Davies. Any errors are mine.
Firmware and Lineage
I'm not able to determine yet anything about the lineage of the firmware. One clue is that it takes a very long time to discover that 1/0 and sqrt(-2) are errors. And the mapping display of the "r" in Error looks more like a Г (G) than a Р (R), but I don't know if that's firmware or a display limitation.
More info at MOSCOW MK-61, and of course Alfred Klomp.