True Q

Amanda Rogers has come aboard the Enterprise to gain some experience prior to entering the Starfleet Academy. She is highly qualified, and beat out hundreds of other candidates for the opportunity. However, she displays an unusual ability: when she is alone in her quarters, she unintentionally causes several puppies to appear, and then sends them away.

It turns out that Amanda is the child of two Q who had taken human form, and Q has been sent to evaluate her: if she is a true Q, she is to go to the Q continuum; if she is some kind of hybrid, she is to be killed.

Ultimately, Q determines that she really is a full Q, but offers her a choice: if she can refrain from using her powers, she can remain on the Enterprise and live out her human life as she chooses; if not, then she must leave with him. Amanda quickly decides that she will live as a human, but when an emergency comes up which threatens the lives of Riker (to whom she has shown a romantic attraction) and La Forge, as well as thousands of others, she uses her power to save them (and to clean the atmosphere of the planet they are orbiting). Realizing that she cannot avoid using her powers, she leaves with Q.

Notes

When Riker is tempted with Q powers in Hide and Q, he too cannot refrain from using them, though he does reject them, in the end.