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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _update_variables_shim_with_recalculation_table(self):
 """ Update self._variables_shim with the final values to be patched into the gate parameters, according to the arithmetic expressions in the original program. For example: DECLARE theta REAL DECLARE beta REAL RZ(3 * theta) 0 RZ(beta+theta) 0 gets translated to: DECLARE theta REAL DECLARE __P REAL[2] RZ(__P[0]) 0 RZ(__P[1]) 0 and the recalculation table will contain: { ParameterAref('__P', 0):
 Mul(3.0, <MemoryReference theta[0]>), ParameterAref('__P', 1):
 Add(<MemoryReference beta[0]>, <MemoryReference theta[0]>) } Let's say we've made the following two function calls: qpu.write_memory(region_name='theta', value=0.5) qpu.write_memory(region_name='beta', value=0.1) After executing this function, our self.variables_shim in the above example would contain the following: { ParameterAref('theta', 0):
 0.5, ParameterAref('beta', 0):
 0.1, ParameterAref('__P', 0):
 1.5, # (3.0) * theta[0] ParameterAref('__P', 1):
 0.6 # beta[0] + theta[0] } Once the _variables_shim is filled, execution continues as with regular binary patching. """

        if not hasattr(self._executable, "recalculation_table"):
            # No recalculation table, no work to be done here.
            return
        for memory_reference, expression in self._executable.recalculation_table.items():
            # Replace the user-declared memory references with any values the user has written,
            # coerced to a float because that is how we declared it.
            self._variables_shim[memory_reference] = float(self._resolve_memory_references(expression))