Singin’ in the Rain is from a wonderful old movie of the same name and you can find it in Alfred Premier Piano Course Book 3. The movie offers a lighthearted depiction of Hollywood in the late 1920s, with the three stars portraying performers caught up in the transition from silent films to “talkies”.
Another version of the same song, sung a bit differently
The Polovtsian Dances form an exotic scene at the end of act 2 of Alexander Borodin’s opera Prince Igor.
The work remained unfinished when the composer died in 1887, although he had worked on it for more than a decade. A performing version was prepared by Nikolai Rimsky-Korsakov and Alexander Glazunov in 1890. One of the more famous dances is found in Piano Pronto Movement 4 and Alfred Premier Piano Course Book 3,.