Plot summary
While the Enterprise investigates the asteroid-laden sector of space of the final battle between the Menthars and the Promellians, it receives a distress call from a Promellian battlecruiser. They find the ancient battlecruiser adrift but intact, and Picard, anxious to see the ship for himself, joins the away team as they transport over. They find a recording by the Promellian captain that suggests the ship was caught in a Menthar trap. After the away team returns to the Enterprise, it begins to suffer a series of power losses that prevent the use of its engines, and is bombarded by radiation that threatens to drain its shields and kill the crew.
Picard orders Chief Engineer Geordi La Forge to find a way to restore power, while a second away team searches for more clues on the Promellian vessel. They discover that the Menthars had used devices to absorb an enemy ship's energy and redirect it back as hazardous radiation, and that the Enterprise is stuck in the same trap.
La Forge realizes that he needs to reconfigure the warp drive, and traces the warp drive's design back to its construction blueprints, created by Dr. Leah Brahms. La Forge enters the ship's holodeck to reason through the engine reconfiguration, where the computer takes an idle remark by Geordi literally and creates a holographic representation of Brahms herself to assist him in his work. He asks the computer to update the hologram with Dr. Brahms' personality profile, and slowly gains romantic feelings for her. Eventually the simulated Dr. Brahms suggests a solution: to allow the computer to take control of the ship, allowing it to make rapid adjustments to compensate for the trap.
La Forge proposes an alternate solution: to reduce the Enterprise ' s power output and maneuver it out of the field by manual control. Picard and La Forge decide that computers cannot account for human intuition and elect to go with the manual approach. Picard takes the helm himself to carry out the operation, successfully moving the Enterprise from the trap. Once free and with power restored, the Enterprise destroys the Promellian craft to prevent others from falling into the trap, and La Forge kisses the simulated Brahms goodbye before turning off the holodeck.
Credits
Adapted from Wikipedia contributors, Booby Trap (Star Trek: The Next Generation). Paragraphs and formatting adjusted; illustrations, reference markers, block quotations and non-story material omitted.