matplotlib
diff --git a/‎lib/matplotlib/backends/registry.py
Lines changed: 9 additions & 3 deletions b/‎lib/matplotlib/backends/registry.py
Lines changed: 9 additions & 3 deletions
diff --git a/‎lib/matplotlib/tests/test_backend_registry.py
Lines changed: 9 additions & 0 deletions b/‎lib/matplotlib/tests/test_backend_registry.py
Lines changed: 9 additions & 0 deletions
diff --git a/‎lib/matplotlib/tests/test_backend_template.py
Lines changed: 11 additions & 0 deletions b/‎lib/matplotlib/tests/test_backend_template.py
Lines changed: 11 additions & 0 deletions
@@ -93,6 +93,9 @@ def __init__(self):
         }
 
     def _backend_module_name(self, backend):
+        if backend.startswith("module://"):
+            return backend[9:]
+
         # Return name of module containing the specified backend.
         # Does not check if the backend is valid, use is_valid_backend for that.
         backend = backend.lower()
@@ -224,7 +227,8 @@ def is_valid_backend(self, backend):
         bool
             True if backend is valid, False otherwise.
         """
-        backend = backend.lower()
+        if not backend.startswith("module://"):
+            backend = backend.lower()
 
         # For backward compatibility, convert ipympl and matplotlib-inline long
         # module:// names to their shortened forms.
@@ -342,7 +346,8 @@ def resolve_backend(self, backend):
             The GUI framework, which will be None for a backend that is non-interactive.
         """
         if isinstance(backend, str):
-            backend = backend.lower()
+            if not backend.startswith("module://"):
+                backend = backend.lower()
         else:  # Might be _auto_backend_sentinel or None
             # Use whatever is already running...
             from matplotlib import get_backend
@@ -395,7 +400,8 @@ def resolve_gui_or_backend(self, gui_or_backend):
         framework : str or None
             The GUI framework, which will be None for a backend that is non-interactive.
         """
-        gui_or_backend = gui_or_backend.lower()
+        if not gui_or_backend.startswith("module://"):
+            gui_or_backend = gui_or_backend.lower()
 
         # First check if it is a gui loop name.
         backend = self.backend_for_gui_framework(gui_or_backend)
 
@@ -86,6 +86,15 @@ def test_is_valid_backend(backend, is_valid):
     assert backend_registry.is_valid_backend(backend) == is_valid
 
 
+@pytest.mark.parametrize("backend, normalized", [
+    ("agg", "matplotlib.backends.backend_agg"),
+    ("QtAgg", "matplotlib.backends.backend_qtagg"),
+    ("module://Anything", "Anything"),
+])
+def test_backend_normalization(backend, normalized):
+    assert backend_registry._backend_module_name(backend) == normalized
+
+
 def test_deprecated_rcsetup_attributes():
     match = "was deprecated in Matplotlib 3.9"
     with pytest.warns(mpl.MatplotlibDeprecationWarning, match=match):
 
@@ -49,3 +49,14 @@ def test_show_old_global_api(monkeypatch):
     mpl.use("module://mpl_test_backend")
     plt.show()
     mock_show.assert_called_with()
+
+
+def test_load_case_sensitive(monkeypatch):
+    mpl_test_backend = SimpleNamespace(**vars(backend_template))
+    mock_show = MagicMock()
+    monkeypatch.setattr(
+        mpl_test_backend.FigureManagerTemplate, "pyplot_show", mock_show)
+    monkeypatch.setitem(sys.modules, "mpl_Test_Backend", mpl_test_backend)
+    mpl.use("module://mpl_Test_Backend")
+    plt.show()
+    mock_show.assert_called_with()