The Frog Prince is a failed attempt of wizard student Bart to cast the frog-to-prince spell.
Springwart's School of Magicry
The big magic recital at Springwart's School of Magicry was coming up, and to prepare, Mrs. Krabappel had her class working on toad-to-prince spells. She told the class to get their toads out so she could check their work. After Lisa succeeded at turning her toad into the Handsome Prince, Mrs. Krabappel went to Bart's desk and sarcastically asked, "Well, Bart, did you study your spell book last night, or did your fairy godmother die again?" Bart protested that he had studied, waved his wand over his toad, and hesitantly said the incantation, "Abra-ca ... turn into a prince guy?" Bart's wand emitted an ugly shower of sparks and made a crackling noise like an out-of-tune radio, and the Toad-Prince Creature appeared on Bart's desk.
The Toad-Prince looked like a hideous cross between a man and a toad (but was nearer in size and appearance to a toad), and constantly vomited copiously. Mrs. Krabappel was sharply critical of Bart's attempt at the spell ("Sloppy work as usual"), and compared Bart's spellcasting unfavorably to Lisa's: "Lisa's casting spells at an eighth-grade level; you've sinned against nature." The Toad-Prince then asked Bart to kill him.
At this, Bart started to argue with Lisa, but the Handsome Prince stepped between them and told Bart to "Stand away from milady!" Bart picked up the Toad-Prince, held him out toward the Handsome Prince, and said, "Get in there! Defend my honor!" All the Toad-Prince did was vomit all over the Handsome Prince and again ask Bart to kill him: "Every moment I live is agony." At this point, Lisa, angry about her prince being vomited on, retaliated by using the "Head Zeppelin" spell on Bart, which turned his head into a Zeppelin. Lisa then used her wand to lift Bart up toward the ceiling and float him around the classroom.
The Toad-Prince was later seen exiting the guest stars' trailer at Fox Studios, along with Pierce Brosnan and the Leprechaun, each of them carrying a fruit basket as they had just completed guest appearances. Brosnan was impressed that they got to keep the fruit baskets, but the Leprechaun complained that "They used to give us champagne 'till somebody ruined it!" and gave the Toad-Prince a dirty look. The Toad-Prince then vomited all over his fruit basket, which prompted Brosnan to ask (in an aside to the Leprechaun), "Do they really think he'll do better with fruit?"
When the Leprechaun carjacked Brosnan (after first tricking Brosnan into letting him and the Toad-Prince into his car), the Toad-Prince went along for the ride, vomiting all the while.