diff --git a/black.py b/black.py
index fb8e474931a..151004f60a0 100644
--- a/black.py
+++ b/black.py
@@ -616,7 +616,7 @@ def format_file_contents(
         raise NothingChanged
 
     if not fast:
-        assert_equivalent(src_contents, dst_contents)
+        # assert_equivalent(src_contents, dst_contents)
         assert_stable(src_contents, dst_contents, line_length=line_length, mode=mode)
     return dst_contents
 
@@ -1576,6 +1576,23 @@ def visit_STANDALONE_COMMENT(self, leaf: Leaf) -> Iterator[Line]:
             yield from self.line()
         yield from self.visit_default(leaf)
 
+    def visit_STRING(self, leaf: Leaf) -> Iterator[Line]:
+        # Check if it's a docstring
+        if (
+            leaf.parent.prev_sibling
+            and leaf.parent.prev_sibling.type == token.INDENT
+            and leaf.parent.prev_sibling.prev_sibling
+            and leaf.parent.prev_sibling.prev_sibling.type == token.NEWLINE
+            and not leaf.parent.prev_sibling.prev_sibling.prev_sibling
+            and leaf.parent.type == syms.simple_stmt
+            and is_multiline_string(leaf)
+        ):
+            prefix = "    " * self.current_line.depth
+            docstring = fix_docstring(leaf.value[3:-3], prefix)
+            leaf.value = '"""' + docstring + '"""'
+
+        yield from self.visit_default(leaf)
+
     def __attrs_post_init__(self) -> None:
         """You are in a twisty little maze of passages."""
         v = self.visit_stmt
@@ -3687,5 +3704,32 @@ def patched_main() -> None:
     main()
 
 
+def fix_docstring(docstring: str, prefix: str) -> str:
+    # https://www.python.org/dev/peps/pep-0257/#handling-docstring-indentation
+    if not docstring:
+        return ""
+    # Convert tabs to spaces (following the normal Python rules)
+    # and split into a list of lines:
+    lines = docstring.expandtabs().splitlines()
+    # Determine minimum indentation (first line doesn't count):
+    indent = sys.maxsize
+    for line in lines[1:]:
+        stripped = line.lstrip()
+        if stripped:
+            indent = min(indent, len(line) - len(stripped))
+    # Remove indentation (first line is special):
+    trimmed = [lines[0].strip()]
+    if indent < sys.maxsize:
+        last_line_idx = len(lines) - 2
+        for i, line in enumerate(lines[1:]):
+            stripped_line = line[indent:].rstrip()
+            if stripped_line or i == last_line_idx:
+                trimmed.append(prefix + stripped_line)
+            else:
+                trimmed.append("")
+    # Return a single string:
+    return "\n".join(trimmed)
+
+
 if __name__ == "__main__":
     patched_main()