diff --git a/qiskit/circuit/parameterexpression.py b/qiskit/circuit/parameterexpression.py
index 71b9fb7761a5..33b24115dee5 100644
--- a/qiskit/circuit/parameterexpression.py
+++ b/qiskit/circuit/parameterexpression.py
@@ -566,24 +566,18 @@ def __eq__(self, other):
     def is_real(self):
         """Return whether the expression is real"""
 
-        # workaround for symengine behavior that const * (0 + 1 * I) is not real
-        # see https://github.com/symengine/symengine.py/issues/414
-        if _optionals.HAS_SYMENGINE and self._symbol_expr.is_real is None:
-            symbol_expr = self._symbol_expr.evalf()
-        else:
-            symbol_expr = self._symbol_expr
-
-        if not symbol_expr.is_real and symbol_expr.is_real is not None:
+        if not self._symbol_expr.is_real and self._symbol_expr.is_real is not None:
             # Symengine returns false for is_real on the expression if
-            # there is a imaginary component (even if that component is 0),
+            # there is an imaginary component (even if that component is 0),
             # but the parameter will evaluate as real. Check that if the
             # expression's is_real attribute returns false that we have a
             # non-zero imaginary
             if _optionals.HAS_SYMENGINE:
-                if symbol_expr.imag == 0.0:
+                if numpy.isclose(float(self._symbol_expr.imag), 0):
+                    self._symbol_expr = self._symbol_expr.real
                     return True
             return False
-        return symbol_expr.is_real
+        return self._symbol_expr.is_real
 
     def sympify(self):
         """Return symbolic expression as a raw Sympy or Symengine object.
diff --git a/requirements.txt b/requirements.txt
index d41eee50ce95..0e809a463735 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -7,8 +7,13 @@ sympy>=1.3
 dill>=0.3
 python-dateutil>=2.8.0
 stevedore>=3.0.0
-typing-extensions; python_version<'3.11'
-# symengine pinning needed due lowered precision handling complex
-# multiplication in version 0.10 wich breaks parameter assignment test
-# (can be removed once issue is fix)
-symengine>=0.9, <0.10; platform_machine == 'x86_64' or platform_machine == 'aarch64' or platform_machine == 'ppc64le' or platform_machine == 'amd64' or platform_machine == 'arm64'
+symengine>=0.10 ; platform_machine == 'x86_64' or platform_machine == 'aarch64' or platform_machine == 'ppc64le' or platform_machine == 'amd64' or platform_machine == 'arm64'
+shared-memory38;python_version<'3.8'
+typing-extensions; python_version < '3.8'
+singledispatchmethod; python_version < '3.8'
+
+# Hack around stevedore being broken by importlib_metadata 5.0; we need to pin
+# the requirements rather than the constraints if we need to cut a release
+# before stevedore is fixed.  `importlib_metadata` is not (currently) a direct
+# requirement of Terra.
+importlib_metadata<5.0; python_version<'3.8'
diff --git a/test/python/circuit/test_parameters.py b/test/python/circuit/test_parameters.py
index 9d14a4d766df..95e92ef40267 100644
--- a/test/python/circuit/test_parameters.py
+++ b/test/python/circuit/test_parameters.py
@@ -1453,31 +1453,30 @@ def test_raise_if_subbing_in_parameter_name_conflict(self):
         with self.assertRaisesRegex(CircuitError, "Name conflict"):
             expr.subs({x: y_second})
 
-    def test_expressions_of_parameter_with_constant(self):
+    @data(2, 1.3, 0, -1, -1.0, numpy.pi, 1j)
+    def test_expressions_of_parameter_with_constant(self, const):
         """Verify operating on a Parameter with a constant."""
 
-        good_constants = [2, 1.3, 0, -1, -1.0, numpy.pi, 1j]
-
         x = Parameter("x")
 
         for op in self.supported_operations:
-            for const in good_constants:
-                expr = op(const, x)
-                bound_expr = expr.bind({x: 2.3})
-
-                self.assertEqual(complex(bound_expr), op(const, 2.3))
-
-                # Division by zero will raise. Tested elsewhere.
-                if const == 0 and op == truediv:
-                    continue
-
-                # Repeat above, swapping position of Parameter and constant.
-                expr = op(x, const)
-                bound_expr = expr.bind({x: 2.3})
-
-                res = complex(bound_expr)
-                expected = op(2.3, const)
-                self.assertTrue(cmath.isclose(res, expected), f"{res} != {expected}")
+            expr = op(const, x)
+            bound_expr = expr.bind({x: 2.3})
+            res = complex(bound_expr)
+            expected = op(const, 2.3)
+            self.assertTrue(cmath.isclose(res, expected), f"{res} != {expected}")
+
+            # Division by zero will raise. Tested elsewhere.
+            if const == 0 and op == truediv:
+                continue
+
+            # Repeat above, swapping position of Parameter and constant.
+            expr = op(x, const)
+            bound_expr = expr.bind({x: 2.3})
+
+            res = complex(bound_expr)
+            expected = op(2.3, const)
+            self.assertTrue(cmath.isclose(res, expected), f"{res} != {expected}")
 
     def test_complex_parameter_bound_to_real(self):
         """Test a complex parameter expression can be real if bound correctly."""