Update documentation for LiteLLM; fix tests

Author: Motta Kin

docs/models/openai.md

@@ -566,7 +566,7 @@ print(result.output)
 
 ### LiteLLM
 
-To use [LiteLLM](https://www.litellm.ai/), set the configs as outlined in the [doc](https://docs.litellm.ai/docs/set_keys). What specific configs you need to set depends on your setup. For example, if you are using a LiteLLM proxy server, then you need to set the `api_base` and `api_key` configs.
+To use [LiteLLM](https://www.litellm.ai/), set the configs as outlined in the [doc](https://docs.litellm.ai/docs/set_keys). In `LiteLLMProvider`, you can pass `api_base` and `api_key`. The value of these configs will depend on your setup. For example, if you are using OpenAI models, then you need to pass `https://api.openai.com/v1` as the `api_base` and your OpenAI API key as the `api_key`. If you are using a LiteLLM proxy server running on your local machine, then you need to pass `http://localhost:<port>` as the `api_base` and your LiteLLM API key as the `api_key`.
 
 Once you have the configs, use the [`LiteLLMProvider`][pydantic_ai.providers.litellm.LiteLLMProvider] as follows:
 
@@ -578,13 +578,14 @@ from pydantic_ai.providers.litellm import LiteLLMProvider
 model = OpenAIChatModel(
     'openai/gpt-3.5-turbo',
     provider=LiteLLMProvider(
-        api_base='<litellm-api-base-url>',
-        api_key='<litellm-api-key>'
+        api_base='<api-base-url>',
+        api_key='<api-key>'
     )
 )
 agent = Agent(model)
 
 result = agent.run_sync('What is the capital of France?')
 print(result.output)
+#> The capital of France is Paris.
 ...
 ```

tests/providers/test_litellm.py

@@ -30,7 +30,6 @@ def test_init_with_custom_llm_provider():
 def test_init_without_api_key():
     provider = LiteLLMProvider()
     assert provider.name == 'litellm'
-    assert provider.base_url == 'https://api.litellm.ai/v1/'
     assert provider.client.api_key == 'litellm-placeholder'