docs: add async tutorial and fix incorrect async usage examples in docstrings

Author: cscguochang

docs/tutorial/async/index.md

@@ -0,0 +1,48 @@
+# Async SQLModel
+
+SQLModel supports asynchronous database operations out of the box using SQLAlchemy's async features and the `AsyncSession` provided by SQLModel.
+
+## When to use Async
+
+Asynchronous programming is particularly useful for Web APIs (like FastAPI) that handle many concurrent connections and spend much of their time waiting for the database to respond.
+
+## Create the Async Engine
+
+To use async, you need an async database driver (like `aiosqlite` for SQLite or `asyncpg` for PostgreSQL).
+
+```python
+from sqlalchemy.ext.asyncio import create_async_engine
+from sqlmodel import SQLModel
+
+sqlite_url = "sqlite+aiosqlite:///database.db"
+engine = create_async_engine(sqlite_url, echo=True)
+
+async def init_db():
+    async with engine.begin() as conn:
+        await conn.run_sync(SQLModel.metadata.create_all)
+```
+
+## Use AsyncSession
+
+Use `from sqlmodel.ext.asyncio.session import AsyncSession` to perform async operations.
+
+```python
+from sqlmodel.ext.asyncio.session import AsyncSession
+from sqlmodel import select
+
+async def get_heroes():
+    async with AsyncSession(engine) as session:
+        statement = select(Hero)
+        results = await session.exec(statement)
+        return results.all()
+```
+
+## Integration with FastAPI
+
+In FastAPI, you can use a dependency to provide an `AsyncSession`:
+
+```python
+async def get_session():
+    async with AsyncSession(engine) as session:
+        yield session
+```

sqlmodel/ext/asyncio/session.py

@@ -116,13 +116,13 @@ async def exec(
         For example:
 
         ```Python
-        heroes = await session.execute(select(Hero)).scalars().all()
+        heroes = (await session.execute(select(Hero))).scalars().all()
         ```
 
         instead you could use `exec()`:
 
         ```Python
-        heroes = await session.exec(select(Hero)).all()
+        heroes = (await session.exec(select(Hero))).all()
         ```
         """
     )
@@ -145,13 +145,13 @@ async def execute(
         For example:
 
         ```Python
-        heroes = await session.execute(select(Hero)).scalars().all()
+        heroes = (await session.execute(select(Hero))).scalars().all()
         ```
 
         instead you could use `exec()`:
 
         ```Python
-        heroes = await session.exec(select(Hero)).all()
+        heroes = (await session.exec(select(Hero))).all()
         ```
         """
         return await super().execute(