docs: Clarify and enhance run_demo_loop utility documentation for beginners

docs/repl.md

@@ -1,6 +1,7 @@
 # REPL utility
 
-The SDK provides `run_demo_loop` for quick interactive testing.
+The SDK provides `run_demo_loop` for quick, interactive testing of an agent's behavior directly in your terminal.
+
 
 ```python
 import asyncio
@@ -14,6 +15,6 @@ if __name__ == "__main__":
     asyncio.run(main())
 ```
 
-`run_demo_loop` prompts for user input in a loop, keeping the conversation
-history between turns. By default it streams model output as it is produced.
-Type `quit` or `exit` (or press `Ctrl-D`) to leave the loop.
+`run_demo_loop` prompts for user input in a loop, keeping the conversation history between turns. By default, it streams model output as it is produced. When you run the example above, run_demo_loop starts an interactive chat session. It continuously asks for your input, remembers the entire conversation history between turns (so your agent knows what's been discussed) and automatically streams the agent's responses to you in real-time as they are generated.
+
+To end this chat session, simply type `quit` or `exit` (and press Enter) or use the `Ctrl-D` keyboard shortcut.

docs/tracing.md

@@ -39,7 +39,7 @@ By default, the SDK traces the following:
 -   Audio outputs (text-to-speech) are wrapped in a `speech_span()`
 -   Related audio spans may be parented under a `speech_group_span()`
 
-By default, the trace is named "Agent workflow". You can set this name if you use `trace`, or you can configure the name and other properties with the [`RunConfig`][agents.run.RunConfig].
+By default, the trace is named "Agent trace". You can set this name if you use `trace`, or you can can configure the name and other properties with the [`RunConfig`][agents.run.RunConfig].
 
 In addition, you can set up [custom trace processors](#custom-tracing-processors) to push traces to other destinations (as a replacement, or secondary destination).
 
@@ -97,6 +97,41 @@ To customize this default setup, to send traces to alternative or additional bac
 1. [`add_trace_processor()`][agents.tracing.add_trace_processor] lets you add an **additional** trace processor that will receive traces and spans as they are ready. This lets you do your own processing in addition to sending traces to OpenAI's backend.
 2. [`set_trace_processors()`][agents.tracing.set_trace_processors] lets you **replace** the default processors with your own trace processors. This means traces will not be sent to the OpenAI backend unless you include a `TracingProcessor` that does so.
 
+
+## Tracing with Non-OpenAI LLMs
+
+You can use an OpenAI API key with non-OpenAI LLMs to enable free tracing on the Openai Traces dashboard without disabling tracing.
+
+```python
+from agents import set_tracing_export_api_key, Agent, Runner, AsyncOpenAI, OpenAIChatCompletionsModel
+from dotenv import load_dotenv
+load_dotenv()
+import os
+
+set_tracing_export_api_key(os.getenv("OPENAI_API_KEY"))
+gemini_api_key = os.getenv("GEMINI_API_KEY")
+
+external_client = AsyncOpenAI(
+    api_key=gemini_api_key,
+    base_url="https://generativelanguage.googleapis.com/v1beta"
+    )
+
+model = OpenAIChatCompletionsModel(
+        model="gemini-2.0-flash",
+        openai_client=external_client,
+    )
+
+agent = Agent(
+    name="Assistant",
+    model=model,
+    )
+```
+
+## Notes
+- Set OPENAI_API_KEY in a .env file.
+- View free traces at Openai Traces dashboard.
+
+
 ## External tracing processors list
 
 -   [Weights & Biases](https://weave-docs.wandb.ai/guides/integrations/openai_agents)
@@ -117,4 +152,3 @@ To customize this default setup, to send traces to alternative or additional bac
 -   [Okahu-Monocle](https://github.com/monocle2ai/monocle)
 -   [Galileo](https://v2docs.galileo.ai/integrations/openai-agent-integration#openai-agent-integration)
 -   [Portkey AI](https://portkey.ai/docs/integrations/agents/openai-agents)
--   [LangDB AI](https://docs.langdb.ai/getting-started/working-with-agent-frameworks/working-with-openai-agents-sdk)