Integrate test from quickstart.

Demos/integrate0.py

+def f(x):
+    return x**2-x
+
+def integrate_f(a, b, N):
+    s = 0.0
+    dx = (b-a)/N
+    for i in range(N):
+        s += f(a+i*dx)
+    return s * dx

Demos/integrate1.pyx

+def f(x):
+    return x**2-x
+
+def integrate_f(a, b, N):
+    s = 0.0
+    dx = (b-a)/N
+    for i in range(N):
+        s += f(a+i*dx)
+    return s * dx

Demos/integrate2.pyx

+cdef double f(double x): except? -2:
+    return x**2-x
+
+def integrate_f(double a, double b, int N):
+    cdef int i
+    s = 0.0
+    dx = (b-a)/N
+    for i in range(N):
+        s += f(a+i*dx)
+    return s * dx

Demos/integrate_timing.py

+import timeit
+
+import integrate0, integrate1, integrate2
+
+number = 10
+py_time = None
+for m in ('integrate0', 'integrate1', 'integrate2'):
+    print m
+    t = min(timeit.repeat("integrate_f(0.0, 10.0, 10000000)", "from %s import integrate_f" % m, number=number))
+    if py_time is None:
+        py_time = t
+    print "    ", t / number, "s"
+    print "    ", py_time / t

docs/src/quickstart/cythonize.rst

@@ -80,7 +80,7 @@ argument in order to pass it.
 Therefore Cython provides a syntax for declaring a C-style function,
 the cdef keyword::
 
-  cdef double f(double) except? -2:
+  cdef double f(double x) except? -2:
       return x**2-x
 
 Some form of except-modifier should usually be added, otherwise Cython