diff --git a/stdlib/2/__builtin__.pyi b/stdlib/2/__builtin__.pyi
index 6bc892f47ba7..9563c32f1b78 100644
--- a/stdlib/2/__builtin__.pyi
+++ b/stdlib/2/__builtin__.pyi
@@ -168,7 +168,7 @@ class int:
     def __rtruediv__(self, x: int) -> float: ...
     def __rmod__(self, x: int) -> int: ...
     def __rdivmod__(self, x: int) -> Tuple[int, int]: ...
-    def __pow__(self, x: int) -> Any: ...  # Return type can be int or float, depending on x.
+    def __pow__(self, x: int, modulo: Optional[int] = ...) -> Any: ...  # Return type can be int or float, depending on x.
     def __rpow__(self, x: int) -> Any: ...
     def __and__(self, n: int) -> int: ...
     def __or__(self, n: int) -> int: ...
@@ -185,6 +185,9 @@ class int:
     def __invert__(self) -> int: ...
     if sys.version_info >= (3,):
         def __round__(self, ndigits: Optional[int] = ...) -> int: ...
+        def __trunc__(self) -> int: ...
+        def __floor__(self) -> int: ...
+        def __ceil__(self) -> int: ...
     def __getnewargs__(self) -> Tuple[int]: ...
 
     def __eq__(self, x: object) -> bool: ...
@@ -242,11 +245,12 @@ class float:
     def __getnewargs__(self) -> Tuple[float]: ...
     if sys.version_info >= (3,):
         @overload
-        def __round__(self) -> int: ...
-        @overload
-        def __round__(self, ndigits: None) -> int: ...
+        def __round__(self, ndigits: None = ...) -> int: ...
         @overload
         def __round__(self, ndigits: int) -> float: ...
+        def __trunc__(self) -> int: ...
+        def __floor__(self) -> int: ...
+        def __ceil__(self) -> int: ...
 
     def __eq__(self, x: object) -> bool: ...
     def __ne__(self, x: object) -> bool: ...
diff --git a/stdlib/2and3/builtins.pyi b/stdlib/2and3/builtins.pyi
index 6bc892f47ba7..9563c32f1b78 100644
--- a/stdlib/2and3/builtins.pyi
+++ b/stdlib/2and3/builtins.pyi
@@ -168,7 +168,7 @@ class int:
     def __rtruediv__(self, x: int) -> float: ...
     def __rmod__(self, x: int) -> int: ...
     def __rdivmod__(self, x: int) -> Tuple[int, int]: ...
-    def __pow__(self, x: int) -> Any: ...  # Return type can be int or float, depending on x.
+    def __pow__(self, x: int, modulo: Optional[int] = ...) -> Any: ...  # Return type can be int or float, depending on x.
     def __rpow__(self, x: int) -> Any: ...
     def __and__(self, n: int) -> int: ...
     def __or__(self, n: int) -> int: ...
@@ -185,6 +185,9 @@ class int:
     def __invert__(self) -> int: ...
     if sys.version_info >= (3,):
         def __round__(self, ndigits: Optional[int] = ...) -> int: ...
+        def __trunc__(self) -> int: ...
+        def __floor__(self) -> int: ...
+        def __ceil__(self) -> int: ...
     def __getnewargs__(self) -> Tuple[int]: ...
 
     def __eq__(self, x: object) -> bool: ...
@@ -242,11 +245,12 @@ class float:
     def __getnewargs__(self) -> Tuple[float]: ...
     if sys.version_info >= (3,):
         @overload
-        def __round__(self) -> int: ...
-        @overload
-        def __round__(self, ndigits: None) -> int: ...
+        def __round__(self, ndigits: None = ...) -> int: ...
         @overload
         def __round__(self, ndigits: int) -> float: ...
+        def __trunc__(self) -> int: ...
+        def __floor__(self) -> int: ...
+        def __ceil__(self) -> int: ...
 
     def __eq__(self, x: object) -> bool: ...
     def __ne__(self, x: object) -> bool: ...
diff --git a/stdlib/2and3/numbers.pyi b/stdlib/2and3/numbers.pyi
index 50b561c24a32..befe7d53a781 100644
--- a/stdlib/2and3/numbers.pyi
+++ b/stdlib/2and3/numbers.pyi
@@ -5,7 +5,7 @@
 # Note: these stubs are incomplete. The more complex type
 # signatures are currently omitted.
 
-from typing import Any, Optional, SupportsFloat
+from typing import Any, Optional, SupportsFloat, overload
 from abc import ABCMeta, abstractmethod
 import sys
 
@@ -70,7 +70,11 @@ class Real(Complex, SupportsFloat):
         @abstractmethod
         def __ceil__(self) -> int: ...
         @abstractmethod
-        def __round__(self, ndigits: Optional[int] = ...): ...
+        @overload
+        def __round__(self, ndigits: None = ...): ...
+        @abstractmethod
+        @overload
+        def __round__(self, ndigits: int): ...
     def __divmod__(self, other): ...
     def __rdivmod__(self, other): ...
     @abstractmethod