docs: add EmpirioLabs AI connection tutorial (LLM Providers)

docs/tutorials/integrations/llm-providers/empiriolabs.md

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+---
+title: "EmpirioLabs AI"
+---
+
+:::warning
+
+This tutorial is a community contribution and is not supported by the Open WebUI team. It serves only as a demonstration on how to customize Open WebUI for your specific use case. Want to contribute? Check out the contributing tutorial.
+
+:::
+
+[EmpirioLabs AI](https://empiriolabs.ai) is an OpenAI-compatible API that hosts open, proprietary, and custom models (Qwen, DeepSeek, GLM, Kimi, MiniMax, Gemma, and more) with pay-as-you-go pricing. Because the API follows the OpenAI Chat Completions format, it works with Open WebUI's built-in OpenAI connection type, and your available models load automatically.
+
+## Prerequisites
+
+- A running Open WebUI instance
+- An EmpirioLabs API key (create one under **API Keys** in the [EmpirioLabs dashboard](https://platform.empiriolabs.ai/dashboard/api-keys))
+
+## Option 1: Connect through the Admin Panel
+
+1. Open the **Admin Panel** and go to **Settings** -> **Connections**.
+2. Under **OpenAI API**, click **+** to add a new connection.
+3. Set the **API Base URL** to:
+
+   ```
+   https://api.empiriolabs.ai/v1
+   ```
+
+4. Paste your EmpirioLabs API key into the **API Key** field.
+5. Save. Open WebUI fetches the model list from the API automatically, so the EmpirioLabs catalog (for example `qwen3-7-plus`, `deepseek-v4-flash`, `glm-5-1`) appears in the model selector.
+
+## Option 2: Configure with environment variables
+
+For Docker deployments, set the connection at startup:
+
+```bash
+docker run -d -p 3000:8080 \
+  -e OPENAI_API_BASE_URL=https://api.empiriolabs.ai/v1 \
+  -e OPENAI_API_KEY=your_empiriolabs_api_key \
+  -v open-webui:/app/backend/data \
+  --name open-webui \
+  ghcr.io/open-webui/open-webui:main
+```
+
+To use EmpirioLabs alongside other OpenAI-compatible endpoints, use the semicolon-separated forms `OPENAI_API_BASE_URLS` and `OPENAI_API_KEYS` instead.
+
+## Verify the connection
+
+1. Open a new chat and pick an EmpirioLabs model from the selector.
+2. Send a message. If you get a response, the connection works.
+3. If the model list is empty, re-check the base URL (it must include `/v1`) and that the API key is valid.
+
+## Notes
+
+- Model ids match the EmpirioLabs catalog at [empiriolabs.ai/models](https://empiriolabs.ai/models); each model page lists pricing, context window, and supported parameters.
+- Reasoning-capable models accept the `reasoning_effort` parameter (`none`, `low`, `medium`, `high`, `max`).
+- Full API reference: [docs.empiriolabs.ai](https://docs.empiriolabs.ai).