I’m fairly confident that the only song that was ever released in the US that mentions a slide rule is Wonderful World, sung by Sam Cooke in 1960.
The last line of the third verse:
“Don’t know what a slide rule is for”
I think it’s safe to say that a lot of people these days can say the same thing.
The name slide rule doesn’t give much hint as to its function, although its function is clear from the name in Japanese, 計算尺.