This phase IV trial compares methadone versus hydromorphone given in the fluid-filled space between the thin layers of tissue that cover the brain and spinal cord (intrathecal) for postoperative pain relief in patients with gynecologic cancer undergo surgery. Methadone binds to opioid receptors in the central nervous system and is a long-acting opioid pain medication. Intrathecal hydromorphone works by changing the way the brain and nervous system respond to pain and is similar to an epidural. This trial may help researchers determine if methadone works as well as intrathecal hydromorphone for pain relief after surgery in patients with gynecologic cancer.