Bop Girl Goes Calypso (1957)

IMDB

Trailer for alternate short title

Basically a time capsule of Pop-Rock, Lounge and Calypso acts this little oddity has a few strange twists.  Judy Tyler, the female lead, is best remembered for her role in "Jailhouse Rock", released the same year. She started her career at age 16 as Princess Summerfall Winterspring on "Howdy Doody". She died in a car crash the same year she made this film.

What takes this flick into the curious column is the linking sequence. Bob (Bobby Troup), a young psychology professor, has developed a machine that can detect pop trends. He "discovers" that Rock and Roll will very soon be eclipsed by Calypso.
His soon to be supplanted girl friend is a cliché sexless professor of Eugenics. (!) She quotes such terrific tomes as 'Mating to Breed: Personality' and 'Mating to Breed: Appearance'. It is a law that these types must unlock their sensual selves in the last reel and she discovers, through the magic of a Bop-Calypso hybrid, that as she says; "hormones trump logic" and goes for Bob's much older mentor professor.

The Goofers, featuring a

dancing/singing trio who do splits and play stand-up bass and trombone while

swinging upside down from ropes.

The Titans do;

'I Wanna Rock and Roll Until I Die'