code: def TR111(rv):
      """Convert f(x)**-i to g(x)**i where either ``i`` is an integer
      or the base is positive and f, g are: tan, cot; sin, csc; or cos, sec.
  
      Examples
      ========
  
      >>> from sympy.simplify.fu import TR111
      >>> from sympy.abc import x
      >>> from sympy import tan
      >>> TR111(1 - 1/tan(x)**2)
      1 - cot(x)**2
  
      """
  
      def f(rv):
          if not (
              isinstance(rv, Pow)
              and (
                  rv.base.is_positive
                  or rv.exp.is_integer
                  and rv.exp.is_negative
              )
          ):
              return rv
  
          if isinstance(rv.base, tan):
              return cot(rv.base.args[0]) ** -rv.exp
          elif isinstance(rv.base, sin):
              return csc(rv.base.args[0]) ** -rv.exp
          elif isinstance(rv.base, cos):
              return sec(rv.base.args[0]) ** -rv.exp
          return rv
  
      return bottom_up(rv, f)
  
imports: from collections import defaultdict
  from sympy.core.add import Add
  from sympy.core.expr import Expr
  from sympy.core.exprtools import Factors, gcd_terms, factor_terms
  from sympy.core.function import expand_mul
  from sympy.core.mul import Mul
  from sympy.core.numbers import pi, I
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.core.sorting import ordered
  from sympy.core.symbol import Dummy
  from sympy.core.sympify import sympify
  from sympy.core.traversal import bottom_up
  from sympy.functions.combinatorial.factorials import binomial
  from sympy.functions.elementary.hyperbolic import cosh, sinh, tanh, coth, sech, csch, HyperbolicFunction
  from sympy.functions.elementary.trigonometric import cos, sin, tan, cot, sec, csc, sqrt, TrigonometricFunction
  from sympy.ntheory.factor_ import perfect_power
  from sympy.polys.polytools import factor
  from sympy.strategies.tree import greedy
  from sympy.strategies.core import identity, debug
  from sympy import SYMPY_DEBUG
label_desc: Use image node_id 24 for calling a global function with example usage: TR111(rv) and returns: bottom_up, rv, rv, unknown, unknown, unknown