Why Is Rapunzel Held Captive By The Witch?

Well now because of 'Tangled' from Disney, it depends on what story you're talking about. In the traditional versions it was because the mother was stealing radishes and the witch had to take something from the mother, which was Rapunzel when she was born, and the witch used Rapunzel for her long hair, but then cut it when she found out Rapunzel had a lover. In the Disney movie 'Tangled'. The queen was really sick and due for a baby any day. So the king and his guards set out to find a magic flower, but the witch (named Mother Gothel) was hoarding the flower for herself so she could stay young forever but when she put the disguise over the flower, she accidently  knocked it over with her lamp, so the guards found it and took it to the queen, which it made her not sick anymore. Few days later they had a baby girl with beautiful golden hair, they named her Rapunzel. One night Mother Gothel went into the castle to see if Rapunzel's hair would make her young just like the flower, it did. Mother Gothel took a pair of scissors and cut a lock of the baby's hair, but when she did it turned brown and lost all it's power so Mother Gothel took Rapunzel and they were never to be seen again. So the reason why Mother Gothel kept Rapunzel is because her hair could heal and make Mother Gothel young forever just as long as Rapunzel would sing the magic song and Mother Gothel was brushing Rapunzel's hair. Hope this helped!

The name "Rapunzel" derives from "rapun" or radish. A pregnant woman develops a craving for radishes and ventures into the garden of a witch to steal some. The witch catches her and demands, in exchange for the mother's life, to be given the baby when it is born. In due course, little Rapunzel is sent to her, and grows up in the witch's house. She has very long hair, and the witch uses this as a rope ladder; every evening she comes home, calls out "Rapunzel, let down your hair!" and climbs up it. One evening this is secretly observed by a young man; at the next opportunity, he imitates the witch's voice, climbs the hair and meets Rapunzel. In some versions, these meetings go on long enough for Rapunzel to become pregnant; in the one usually given to children, the witch soon finds out, cuts off the hair, lures the lover to climb it and then lets him fall. He falls in a thorn bush and is blinded.
The usual ending to the story is that Rapunzel escapes, finds her lover and restores his sight with herbs, or in some versions, her tears.

What did the witch give rapunzel mother in exchange of a baby?