Docetaxel, Prednisone, and Vatalanib in Treating Patients With Advanced Prostate Cancer

DISEASE CHARACTERISTICS: * Histologically documented adenocarcinoma of the prostate * Progressive, systemic (metastatic) disease despite castrate levels of testosterone due to orchiectomy or luteinizing-hormone releasing hormone (LHRH) agonist, meeting 1 of the following criteria: * Measurable disease, defined as any lesion that can be accurately measured in at least 1 dimension ≥ 2 cm by conventional techniques or ≥ 1 cm by spiral CT scan or MRI * Nonmeasurable disease with PSA ≥ 5 ng/mL * Bone lesions * Pleural or pericardial effusions, ascites * CNS lesions, leptomeningeal disease * Irradiated lesions, unless progression documented after radiotherapy * No PSA ≥ 5 ng/mL as only evidence of disease * PSA evidence for progressive prostate cancer consists of a PSA level ≥ 5 ng/mL that has risen on ≥ 2 successive occasions, ≥ 2 weeks apart * Castrate levels of testosterone (\< 50 ng/dL) must be maintained * If no prior orchiectomy, patients must remain on testicular androgen suppression (e.g., with an LHRH analogue) * Patients receiving an antiandrogen as part of primary androgen ablation must demonstrate disease progression after discontinuation of antiandrogen * Disease progression after antiandrogen withdrawal is defined as 2 consecutive rising PSA values, obtained at least 2 weeks apart, or documented osseous or soft tissue progression * For patients receiving flutamide or megestrol acetate, at least 1 of the PSA values must be obtained 4 weeks or more after flutamide/megestrol acetate discontinuation * For patients receiving bicalutamide or nilutamide, at least 1 of the PSA values must be obtained 6 weeks or more after antiandrogen discontinuation * If improvement after antiandrogen withdrawal is noted, disease progression must be established * No pleural effusion or ascites that causes respiratory compromise ( ≥ grade 2 dyspnea) * No history of CNS disease, including primary brain tumor, seizures, or carcinomatous meningitis PATIENT CHARACTERISTICS: * Fertile patients must use effective barrier contraception during and for 3 months after completion of study treatment * Karnofsky performance status ≥ 60% * Life expectancy \> 12 weeks * Granulocyte count \> 1,500/mm\^3 * Platelet count \> 75,000/mm\^3 * Hemoglobin \> 8.0 g/dL * Creatinine \< 1.5 times upper limit of normal (ULN) * Bilirubin \< 1.5 times ULN * SGOT/SGPT \< 1.5 times ULN * Urinalysis ≤ 1+ proteinuria based on dipstick reading OR 2+ proteinuria on dipstick reading AND total urinary protein ≤ 3,500 mg on 24 hour urine collection and creatinine clearance ≥ 50 mL/min on a 24-hour urine collection * No impairment of gastrointestinal (GI) function or GI disease that may affect or alter absorption of vatalanib (i.e., malabsorption syndromes) * No myocardial infarction or significant change in anginal pattern within the last 6 months, symptomatic congestive heart failure (New York Heart Association class III or IV), or uncontrolled cardiac arrhythmia * No pre-existing grade 3 or 4 clinical peripheral neuropathy * No history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80 * No deep vein thrombosis or pulmonary embolus within the past year * No poorly controlled diabetes (fasting blood glucose \> 250) despite optimization of medical therapy * No labile or poorly controlled hypertension (systolic blood pressure \> 160 mm Hg, diastolic blood pressure \> 90 mm Hg) despite maximal management with anti-hypertensives * No serious uncontrolled, concurrent medical illness, including ongoing or active infection * Patients on Suppressive antibiotic therapy for chronic urinary tract infection are eligible * No psychiatric illness or social situation that would limit compliance with treatment * No "currently active" second malignancy other than nonmelanoma skin cancers * Not considered "currently active" if competed therapy and at \< 30% risk of relapse * No interstitial pneumonia or extensive and symptomatic interstitial fibrosis of the lung PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No grapefruit or grapefruit juice during study treatment * No history of gastrectomy/small bowel resection * At least 4 weeks since prior hormonal therapy, including ketoconazole, aminoglutethimide, systemic steroids (any dose), and megestrol acetate (any dose) * At least 4 weeks since prior drug or herbal product known to decrease PSA levels (e.g., finasteride, saw palmetto, or PC-SPES) * At least 4 weeks since prior major surgery and fully recovered * At least 4 weeks since prior radiation therapy and fully recovered * At least 8 weeks since the last dose of prior strontium chloride Sr 89 or samarium Sm 153 lexidronam pentasodium * Patients receiving bisphosphonate therapy prior to initiating protocol treatment must have received bisphosphonates for at least the past month * No bisphosphonate initiation for 1 month prior to and during study treatment * No prior systemic chemotherapy for prostate cancer * No prior antiangiogenic agents (thalidomide, bevacizumab) * No other concurrent chemotherapy, investigational agents, radiotherapy (including palliative), or biologic therapy * No biologic therapy or immunotherapy ≤ 4 weeks prior to study treatment * No more than 1 prior therapy with an investigational agent, completed ≥ 4 weeks prior to study treatment * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent therapeutic warfarin or similar oral anticoagulant that is metabolized by the cytochrome p450 system * Heparin is allowed * No other concurrent hormonal therapy except for the following: * Steroids for adrenal failure * Hormones for nondisease-related conditions (e.g., insulin for diabetes) * Intermittent dexamethasone