Carboplatin, Paclitaxel, and Bevacizumab in Treating Patients With Stage IV Melanoma That Cannot Be Removed By Surgery

Inclusion Criteria: * Histologically confirmed melanoma * Unresectable stage IV disease * Evidence of metastatic disease * Measurable disease, defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm by spiral CT scan * No radiologically confirmed invasion of adjacent organs (e.g., duodenum or stomach) * No tumor invasion of major blood vessels * No history of primary brain tumor or other CNS disease * No brain metastases by MRI or CT scan * Performance status - ECOG 0-2 * More than 4 months * Absolute granulocyte count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Hemoglobin ≥ 9 g/dL (transfusion allowed) * No active bleeding * Bilirubin ≤ 1.5 mg/dL * AST ≤ 3 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 3 times ULN * INR ≤ 1.5 times ULN * PTT normal * No known esophageal varices * Creatinine ≤ 1.5 times ULN * Urine protein creatinine ratio ≤ 0.5 * Urine protein \< 1 g/24-hr urine collection * No New York Heart Association class II-IV congestive heart failure * No serious cardiac arrhythmia requiring medication * No myocardial infarction within the past 6 months * No unstable angina within the past 6 months * No clinically significant peripheral vascular disease * No uncontrolled hypertension (i.e., blood pressure ≥ 150/90 mmHg despite antihypertensive therapy) * No clinically significant stroke within the past 6 months * No deep vein thrombosis within the past year * No other vascular abnormality * No pulmonary embolus within the past year * No history of abdominal fistula * No gastrointestinal perforation * No intra-abdominal abscess within the past 4 weeks * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 6 months after completion of study therapy * No other pathological condition that would confer a high risk of bleeding * No active infection requiring parenteral antibiotics * No serious nonhealing wound (including wounds healing by secondary intention), ulcer, or bone fracture * No peripheral neuropathy ≥ grade 2 * No history of allergic reaction attributed to compounds of similar chemical or biological composition to the study drugs * No uncontrolled seizures * No other uncontrolled illness * No significant traumatic injury within the past 4 weeks * No prior antivascular endothelial growth factors (VEGF), including any of the following: * Bevacizumab * VEGF Trap * Anti-VEGF receptor monoclonal antibody * Small molecular tyrosine kinase inhibitors of VEGF receptors * No more than 1 prior systemic chemotherapy regimen * No prior carboplatin or paclitaxel * No other concurrent chemotherapy * More than 4 weeks since prior radiotherapy * No prior radiotherapy to \> 25% of bone marrow * No concurrent radiotherapy * At least 4 weeks since prior major surgical procedure or open biopsy * At least 1 week since prior fine-needle aspiration or core biopsy * No concurrent major surgery * More than 4 weeks since prior systemic therapy * No concurrent full-dose oral or parenteral anticoagulation * No concurrent antiplatelet therapy except low-dose aspirin (i.e., 81 mg of oral aspirin daily) allowed * No other concurrent experimental drugs