This phase II trial tests whether reduced dose radiation therapy after transoral robotic surgery works in treating patients with human papillomavirus (HPV)-positive oropharyngeal cancer. HPV positive oropharyngeal cancer has a better prognosis than oropharyngeal cancer not caused by HPV. A standard of care treatment for HPV positive oropharyngeal cancer is transoral robotic surgery followed by radiation therapy. However, this treatment is associated with many long-term side effects including difficulty swallowing. Radiation therapy uses high energy rays to kill tumor cells and shrink tumors. Giving reduced dose radiation therapy after transoral robotic surgery may improve swallowing outcomes and quality of life compared to standard of care dose radiation therapy after transoral robotic surgery.