PYTHON-3471 Test Support for Gevent in Python 3.11 (#1091)

Author: blink1073

.evergreen/config.yml

@@ -2614,12 +2614,26 @@ buildvariants:
   exclude_spec:
    # Don't test green frameworks on these Python versions.
    - platform: ubuntu-18.04
-     python-version: ["pypy3.7", "pypy3.8"]
+     python-version: ["pypy3.7", "pypy3.8", "3.11"]
      green-framework: "*"
      auth-ssl: "*"
   display_name: "${green-framework} ${python-version} ${platform} ${auth-ssl}"
   tasks: *all-server-versions
 
+- matrix_name: "tests-python-version-green-framework-ubuntu20"
+  matrix_spec:
+    platform: ubuntu-20.04
+    python-version: ["3.11"]
+    green-framework: "*"
+    auth-ssl: "*"
+  display_name: "${green-framework} ${python-version} ${platform} ${auth-ssl}"
+  tasks:
+    - ".rapid"
+    - ".latest"
+    - ".6.0"
+    - ".5.0"
+    - ".4.4"
+
 - matrix_name: "tests-windows-python-version"
   matrix_spec:
     platform: windows-64-vsMulti-small