Paclitaxel, Bevacizumab And Adjuvant Intraperitoneal Carboplatin in Treating Patients Who Had Initial Debulking Surgery for Stage II, Stage III, or Stage IV Ovarian Epithelial, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Histologically confirmed ovarian epithelial, primary peritoneal, or fallopian tube cancer * Stage II-IV disease * The following histologic epithelial cell types are eligible: * Serous adenocarcinoma * Mucinous adenocarcinoma * Clear cell adenocarcinoma * Transitional cell carcinoma * Adenocarcinoma not otherwise specified * Endometrioid adenocarcinoma * Undifferentiated carcinoma * Mixed epithelial carcinoma * Malignant Brenner's tumor * Optimal (≤ 1 cm residual disease) OR suboptimal residual disease after initial debulking surgery (performed within the past 12 weeks) * Synchronous primary endometrial cancer OR prior history of endometrial cancer allowed provided all of the following are true: * Stage IB disease or less * Less than 3 mm invasion without vascular or lymphatic invasion * No poorly differentiated subtypes, including the following: * Papillary serous * Clear cell * Other FIGO grade 3 lesions * No epithelial tumors of low malignant potential (borderline tumors) * No CNS disease, including primary brain tumor, seizures not controlled with standard medical therapy, or brain metastases by history or evidence upon physical examination within the past 6 months * Performance status - GOG 0-2 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * INR ≤ 1.5 * PTT \< 1.2 times upper limit of normal (ULN) * No active bleeding or pathologic conditions carrying high risk of bleeding (e.g.,…