DISEASE CHARACTERISTICS: - Histologically confirmed ovarian epithelial, primary peritoneal, or fallopian tube cancer - FIGO stage III with > 1 cm residual ("suboptimally debulked" disease) OR FIGO stage IV disease, defined surgically after completion of initial abdominal surgery* NOTE: *The minimum surgery required is an abdominal surgery providing tissue for histological evaluation and establishing and documenting the primary site and stage, as well as a maximal effort at tumor debulking in stage III and IV disease. If additional surgery was performed, it should have been in accordance with appropriate surgery for ovarian and peritoneal carcinoma described in the GOG Surgical Procedures Manual. - The following histologic epithelial cell types are eligible: - Serous - Endometrioid - Clear cell** - Mucinous adenocarcinoma** - Undifferentiated carcinoma - Mixed epithelial carcinoma - Transitional cell carcinoma - Malignant Brenner tumor - Adenocarcinoma not otherwise specified - The histologic features of the tumor must be compatible with a primary Müllerian epithelial adenocarcinoma NOTE: **Patients with clear cell and mucinous tumors are eligible provided there is no higher priority study. - Co-existing fallopian tube carcinoma in situ allowed provided the primary origin of invasive tumor is ovarian, primary peritoneal, or fallopian tube - No current diagnosis of borderline ovarian epithelial tumor (BOET; formerly "tumors of low malignant potential") or recurrent invasive ovarian epithelial, primary peritoneal, or fallopian tube cancer treated with surgery only (e.g., stage Ia or Ib low-grade ovarian epithelial or fallopian tube cancers) - Prior diagnosis of BOET that was surgically resected and an unrelated, new invasive cancer is diagnosed allowed provided no prior chemotherapy for ovarian cancer was administered - Patients will not be eligible for therapy on other clinical trials evaluating consolidation or maintenance therapy - No history or evidence upon physical examination of CNS disease, including primary brain tumor, seizures not controlled with standard medical therapy, or any brain metastases (for patients who elect to receive bevacizumab) PATIENT CHARACTERISTICS: - GOG performance status 0-2 - ANC ≥ 1,500/mm^3 (not induced or supported by granulocyte colony-stimulating factors) - Platelet count ≥ 100,000/mm^3 - Creatinine ≤ 1.5 times upper limit of normal (ULN) - Bilirubin ≤ 1.5 times ULN - SGOT ≤ 3 times ULN - Alkaline phosphatase ≤ 2.5 times ULN - Not pregnant or nursing - Negative pregnancy test - Fertile patients must use effective contraception during and for ≥ 6 months after completion of study treatment - No neuropathy (sensory or motor) > CTCAE grade 1 - No synchronous primary endometrial cancer or a history of primary endometrial cancer, unless all of the following conditions are met: - Stage not greater than Ia - Grade 1 or 2 - No more than superficial myometrial invasion - No vascular or lymphatic invasion - No poorly differentiated subtypes, including papillary serous, clear cell, or other FIGO grade 3 lesions - No other invasive malignancies with any evidence of the cancer present within the past 5 years except for nonmelanoma skin cancer - No acute hepatitis or active infection that requires parenteral antibiotics - No clinically significant cardiovascular disease, including: - Myocardial infarction or unstable angina within the past 6 months - NYHA class II-IV congestive heart failure - Serious cardiac arrhythmia requiring medication (this does not include asymptomatic, atrial fibrillation with controlled ventricular rate) - No other medical history or conditions that, in the opinion of the investigator, should exclude participation in this study - Patients who elect to receive bevacizumab must meet the following criteria: - PT such that INR is ≤ 1.5 (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin for management of venous thrombosis including pulmonary thromboembolus) - PTT < 1.2 times ULN - No clinically significant proteinuria (i.e., urine protein-creatinine ratio < 1.0) - No serious non-healing wound, ulcer, or bone fracture (including a history of abdominal fistula, gastrointestinal [GI] perforation, or intra-abdominal abscess) within the past 28 days - Patients with granulating incisions healing by secondary intention with no evidence of fascial dehiscence or infection are eligible but require weekly wound examinations - No active bleeding or pathologic conditions that carry high risk of bleeding (e.g., known bleeding disorder, coagulopathy, or tumor involving major vessels) - No metastatic tumor in the parenchyma of the liver or lungs with proximity to large vessels that could make the patients at high risk of lethal hemorrhage during treatment with bevacizumab (i.e., hemoptysis, liver rupture) - No cerebrovascular accident (e.g., stroke), transient ischemic attack, or subarachnoid hemorrhage within the past 6 months - No peripheral vascular disease ≥ CTCAE grade 2 (at least brief [< 24 hours] episodes of ischemia managed non-surgically and without permanent deficit) - No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies - No known allergy to cremophor or polysorbate 80 - No significant traumatic injury within 28 days before beginning bevacizumab - No patients with clinical symptoms or signs of GI obstruction AND who require parenteral hydration and/or nutrition PRIOR CONCURRENT THERAPY: - See Disease Characteristics - No more than 12 weeks since diagnostic/staging surgery - No prior cancer treatment that contraindicates study treatment - No prior radiotherapy to any portion of the abdominal cavity or pelvis - Prior radiotherapy for localized cancer of the breast, head and neck, or skin is allowed provided that it was completed > 3 years ago and that the patient remains free of recurrent or metastatic disease - No prior chemotherapy for any abdominal or pelvic tumor, including neoadjuvant chemotherapy for ovarian, primary peritoneal, or fallopian tube cancer - Prior adjuvant chemotherapy for localized breast cancer allowed provided that it was completed > 3 years ago and that the patient remains free of recurrent or metastatic disease - No prior targeted therapy (including, but not limited to, vaccines, antibodies, tyrosine kinase inhibitors) or hormonal therapy for management of ovarian epithelial, fallopian tube, or primary peritoneal cancer - No prior therapy with any anti-VEGF drug, including bevacizumab - No concurrent reassessment or cytoreductive surgery - No other concurrent antineoplastic therapy including cytotoxic, biologic, hormonal, or radiation therapy - No concurrent thrombopoietic agents - No concurrent amifostine or other protective agents - Patients who elect to receive bevacizumab must meet the following criteria: - No major surgical procedure or open biopsy within 28 days before beginning bevacizumab - No tissue biopsy (e.g., core biopsy) within 7 days before beginning bevacizumab - Concurrent ovarian estrogen with or without progestin replacement therapy as indicated at the lowest effective dose(s) for control of menopausal symptoms allowed - No high-dose progestins for management of anorexia while on study treatment or before disease progression - No concurrent major surgical procedure including, but not limited to, any of the following: - Abdominal surgery (laparotomy or laparoscopy) before disease progression - Colostomy or enterostomy reversal - Interval or secondary cytoreductive surgery - Second-look surgery - Concurrent heparin, lovenox, or alternative anticoagulants allowed