Electrical engineer, most introvert job?
"analyses and calculations" eh?
Well there's a whole LOAD of EE jobs where you might
need to spend a LOT of time doing bureaucratic / regulatory
oriented analyses and calculations e.g. medical devices
that need FDA or other kinds of approvals, avionics where
you have to go through a lot of FAA or other kinds of
process / documentation, safety regulated stuff like
equipment for use in explosive environments or so on.
Now if you're just talking about TECHNICAL calculations
and analyses that aren't mostly related to compliance
or regulatory engineering...
Microwave design tends to involve a fair amount of
modeling especially at the higher frequencies for the more
complex systems, satellites, etc.
Quantum electronics design, potentially.
DSP implementations that involve EE or complex
mixed signal signal processing design.
Doing IC design involves a lot of simulations and analyses
usually, especially very high speed stuff or mixed
signal stuff at high density and high performance.