Patient description: The patient is a 37-year-old woman who came to the clinic for a routine Pap smear. The test revealed stage 1B of cervical cancer. The patient tested positive for HPV 16. She has three sexual partners and four children. She underwent tubal ligation. She smokes 30 packs/year and drinks alcohol frequently. She is otherwise healthy. She was offered a radical hysterectomy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Borderline Ovarian Mucinous Tumor Ovarian Mucinous Cystadenocarcinoma Recurrent Fallopian Tube Carcinoma Recurrent Ovarian Carcinoma Stage IA Fallopian Tube Cancer AJCC v6 and v7 Stage IA Ovarian Cancer AJCC v6 and v7 Stage IB Fallopian Tube Cancer AJCC v6 and v7 Stage IB Ovarian Cancer AJCC v6 and v7 Stage IC Fallopian Tube Cancer AJCC v6 and v7 Stage IC Ovarian Cancer AJCC v6 and v7 Stage IIA Fallopian Tube Cancer AJCC v6 and v7 Stage IIA Ovarian Cancer AJCC V6 and v7 Stage IIB Fallopian Tube Cancer AJCC v6 and v7 Stage IIB Ovarian Cancer AJCC v6 and v7 Stage IIC Fallopian Tube Cancer AJCC v6 and v7 Stage IIC Ovarian Cancer AJCC v6 and v7 Stage IIIA Fallopian Tube Cancer AJCC v7 Stage IIIA Ovarian Cancer AJCC v6 and v7 Stage IIIB Fallopian Tube Cancer AJCC v7 Stage IIIB Ovarian Cancer AJCC v6 and v7 Stage IIIC Fallopian Tube Cancer AJCC v7 Stage IIIC Ovarian Cancer AJCC v6 and v7 Stage IV Fallopian Tube Cancer AJCC v6 and v7 Stage IV Ovarian Cancer AJCC v6 and v7 Patients with a histologic diagnosis of mucinous adenocarcinoma of the ovary or fallopian tube with either optimal (=< 1 cm residual disease) or suboptimal residual disease following initial surgery; patients may have measurable disease as defined by Response Evaluation in Solid Tumors (RECIST) 1.1 or no measurable disease All patients must have had appropriate surgery including appendectomy (unless patient has history of prior appendectomy) for ovarian or fallopian tube carcinoma with appropriate tissue available for histologic evaluation to confirm diagnosis and stage Patients must have stage II-IV disease (new or recurrent-chemonaïve; no brain metastasis) or recurrent stage I disease (chemonaïve) Newly diagnosed patients must begin protocol therapy within 10 weeks of primary debulking; for stage I recurrent patients (chemonaïve), they should begin protocol therapy within 14 days of randomization Patients must have a negative colonoscopy within 1 year of enrolling in the study Absolute neutrophil count (ANC) >= 1,500/mcl White blood cell (WBC) count >= 3,000/mcl Platelets >= 100,000/mcl Hemoglobin (Hgb) >= 10 g/dl (can be post transfusion) Creatinine less than or equal to 1.5 x institutional upper limit normal (ULN) OR creatinine clearance > 50 cc/min  Patients with known colon cancer or history of colon cancer Patients with primary peritoneal carcinoma Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancer, are excluded if there is any evidence of other malignancy being present within the last 5 years; patients are also excluded if their previous cancer treatment contraindicates this protocol therapy Patients who have received chemotherapy, radiotherapy or any investigational treatment for a gynecologic cancer (does breast cancer) or colorectal cancer prior to enrollment Patients with a major surgical procedure anticipated during the course of the study; this includes but is not limited to: abdominal surgery (laparotomy or laparoscopy) such as colostomy or enterostomy reversal, interval or secondary cytoreductive surgery, or second look surgery; please consult with the study chair prior to patient entry for any questions related to the classification of surgical procedures Patients may have minor surgical procedures (i.e., mediport insertion) fine needle aspiration or core biopsies as long as it is performed > 7 days prior to the first date of bevacizumab therapy and there is no evidence of wound disruption or impaired healing Patients with surgery (including open biopsy) within 4 weeks prior to anticipated first dose of bevacizumab (allowing for fact that bevacizumab can be omitted from first cycle of chemotherapy) Patients with a history of abdominal fistula or perforation within the past 12 months Patients with a current, serious, non-healing wound, ulcer, or bone fracture; patients with granulating incisions healing by secondary intention with no evidence of fascial dehiscence or infection are eligible but require weekly wound examinations Patients with known hypersensitivity to Chinese hamster cell products or other recombinant human or humanized antibodies