fix: substitute server variable defaults when building base URL from OpenAPI spec (#3770)

* fix: resolve OpenAPI 3.x server variables in _create_default_client

When an OpenAPI spec defines server variables (e.g. `https://{region}.api.example.com/v1`),
the default values are now substituted before constructing the httpx client base URL.
Previously, the URL was used as-is, causing all requests to fail for specs that use
server variable templating.

Fixes #1681

* fix: use str.replace instead of format_map for server variable substitution

format_map applies Python string formatting rules, so variable names
like {api.version} would be treated as attribute access and raise errors.
Literal token replacement handles all valid OpenAPI variable names safely.

src/fastmcp/server/providers/openapi/provider.py

@@ -175,6 +175,9 @@ class OpenAPIProvider(Provider):
                 "entry to the spec or provide an httpx.AsyncClient explicitly."
             )
         base_url = servers[0]["url"]
+        variables = servers[0].get("variables", {})
+        for name, var in variables.items():
+            base_url = base_url.replace(f"{{{name}}}", var.get("default", ""))
         return httpx.AsyncClient(base_url=base_url, timeout=DEFAULT_TIMEOUT)
 
     @asynccontextmanager

tests/server/providers/openapi/test_server.py

@@ -9,6 +9,58 @@ from fastmcp.server.providers.openapi import OpenAPIProvider
 from fastmcp.server.providers.openapi.provider import DEFAULT_TIMEOUT
 
 
+class TestOpenAPIProviderServerVariables:
+    """Test that OpenAPIProvider resolves OpenAPI 3.x server variables."""
+
+    def test_server_variables_substituted_with_defaults(self):
+        spec = {
+            "openapi": "3.0.0",
+            "info": {"title": "Test API", "version": "1.0.0"},
+            "servers": [
+                {
+                    "url": "https://{region}.api.example.com/v1",
+                    "variables": {
+                        "region": {
+                            "default": "us",
+                            "enum": ["us", "eu", "apac"],
+                        }
+                    },
+                }
+            ],
+            "paths": {},
+        }
+        client = OpenAPIProvider._create_default_client(spec)
+        assert str(client.base_url) == "https://us.api.example.com/v1/"
+
+    def test_multiple_server_variables_substituted(self):
+        spec = {
+            "openapi": "3.0.0",
+            "info": {"title": "Test API", "version": "1.0.0"},
+            "servers": [
+                {
+                    "url": "{scheme}://{host}/v1",
+                    "variables": {
+                        "scheme": {"default": "https"},
+                        "host": {"default": "api.example.com"},
+                    },
+                }
+            ],
+            "paths": {},
+        }
+        client = OpenAPIProvider._create_default_client(spec)
+        assert str(client.base_url) == "https://api.example.com/v1/"
+
+    def test_static_server_url_unaffected(self):
+        spec = {
+            "openapi": "3.0.0",
+            "info": {"title": "Test API", "version": "1.0.0"},
+            "servers": [{"url": "https://api.example.com"}],
+            "paths": {},
+        }
+        client = OpenAPIProvider._create_default_client(spec)
+        assert str(client.base_url) == "https://api.example.com"
+
+
 class TestOpenAPIProviderBasicFunctionality:
     """Test basic OpenAPIProvider functionality."""