The Prisoner of Benda is the tenth episode of the sixth season of Futurama. The Professor invents a mind switching machine. All the main characters end up switching bodies for various reasons.
"Hey, have you seen the professor? I think he may have my body."
"Well, he talked about running away, and then he ran way."
Leela accuses Fry of only caring about her looks and Fry tries talk his way out of this argument while Bender interrupts claiming he's going to try to steal the Robo-Hungarian Emperor's crown. Meanwhile, Amy and the professor switch bodies so the professor can have fun and Amy can pig out. When they try to switch back they find out they can't because the same bodies can't switch twice. Farnsworth in Amy's body switches with Bender to try and fix it but he realizes it won't work. As the professor tries to figure it out, Amy continues to eat and Bender goes to seduce the guard on board the Emperor's yacht to steal the crown. He finds out the Emperor is tired of the rich life and wants to live a regular life so Bender takes him back to the office.
However, the professor decides to run away in Bender's invincible body and joins the circus as a daredevil. Leela and Amy in the professor's body switch so Leela can get the senior citizen's discount at the movies and Amy can continue to eat because the body of an old man can't digest anything. When Fry finds out Leela gets even more enraged at him about his shallowness. To get back at her, Fry switches with Zoidberg and Fry and Leela get disgusted at each other's appearance but deny it and challenge each other to a romantic dinner. Meanwhile, Bender in Amy's body switches with Scruffy's robotic washbucket and then with the Emperor. Zoidberg in Fry's body and the Emperor in Washbucket's body pretend to recognize each other and they go back to the apartment.
Zoidberg rips the dishwasher out of the wall spewing water everywhere and then does the same with the oven to try to boil the water but gas begins to leak as well. The Emperor lights up a cigar causing the apartment to explode. Meanwhile Washbucket in Amy's body tries to seduce Scruffy because she loves him but he reluctantly and nobly rejects her because deep down she is still janitorial equipment. He then starts to cry. Bender discovers that the emperor's fiancee is cheating on him with the emperor's cousin and plan to take the throne. Bender escapes and is chased through the streets under the exploding apartment to the U.N. Meanwhile Hermes discovers Amy in the body of a grossly overweight Leela gorging herself on butter. Amy is depressed because she can't stop eating, so Hermes switches with her to help Leela's body drop the pounds, commenting that she can't really make his body any worse than it already is. At Elzar's restaurant, Fry in Zoidberg's body and Leela in the professor's body are trying to gross each other out and when Fry argues that he's as attracted to Leela as ever he begins to make out with her on the table. Amy in Hermes' body looks on in horror, instantly put off her pork sundae.
After returning to Leela's apartment, having sex, and at the same time using their own minds to effectively rape Zoidberg's and Farnsworth's bodies, Fry and Leela turn on the T.V. to discover Bender's situation on the news. Meanwhile, at the circus, Farnsworth meets an old cannon named Big Bertha who loves her old body and wouldn't trade it for anything in the world. As all the Robo-Hungarian carnies watch the scene at the U.N. on the news. Big Bertha launches the professor even though it shatters her body so he can get there in time to save the emperor's body. He crashes through the roof and using the tiny robot carnies he hid in his breast plate, slices the emperor's cousin to pieces. Back at the office, the Harlem Globetrotters help the crew return to their original bodies. They discover Amy helped Hermes' body lose weight after losing her appetite forever after watching the scene at Elzar's. This inspired Hermes' to do the same for Leela's body. In the end, everyone goes back to their original body and Bender realizes he left the emperor's real crown in the emperor's breastplate and begins to think of a new scheme to steal it again.
The order of who got switched into who's body and why is as follows:
Farnsworth and Amy switch so Amy can pig out in Farnsworth's body.
Bender and Amy (with Farnsworth's mind) switch so that Bender can pull off his heist to take the Emperor's crown.
Farnsworth (with Amy's mind) switches with Leela so that Leela can get a discount at the movies because she "hates paying 14 dollars to watch Nicolas Cage solve things" while Amy can actually digest the food she is gorging herself on.
Amy (with Bender's mind) switches with Scruffy's Washbucket so that Bender and the Emperor can switch bodies. Washbucket agrees presumably for the chance to seduce Scruffy in Amy's body.
Zoidberg and Fry switch so that Fry can prove that Leela only finds him attractive because of his looks as well. Fry actually uses Zoidberg's body to make love with Leela who was in Farnsworth's body at the time.
Washbucket (with Bender's mind) and the Emperor swich bodies so the Emperor can be an Average Joe for a day and Bender can get the Emperor's money.
Leela (with Amy's mind) switches with Hermes because Amy was making Leela fat and Hermes thinks he can loose the weight that Amy gained.