The purpose of this study is to determine the maximum tolerated dose (MTD) of intravenous weekly paclitaxel given with intravenous carboplatin and bevacizumab in patients with epithelial ovarian, primary peritoneal, or fallopian tube carcinoma that are to receive neoadjuvant chemotherapy (prior to surgical cytoreduction). Patients will then undergo surgery which will allow an objective measure of response to the above regimen as well as assessment of surgical outcomes.