What is the calculator's exact syntax for integration and derivatives?

Yes, that is so true, thanks Alan :)

I have just added this thread to our reference material Sticky Topic    

Indefinite integral:  int(f(x))   e.g.  int(x^2)

Definite integral: int(f(x),x=a..b)   e.g.  int(x^2,x=0..1)

Differentiation;  diff(f(x))   e.g.  diff(x^2)

(Thanks to Chris who just initiated my search for these!)

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Thanks, Alan......

I should add that Alan is our resident "Calculator Guru".....if  it can be done....he'll usually discover it....!!!

Warning!!

Beware of definite integration using trigonometric functions.  web2.0calc insists on treating the arguments to trig functions in degrees.  This leads to problems for definite integrals.  

For example 

$$\int_0^1{cos(x)}dx=0.841$$   

However, webcalc gives:

$$\int_{{\mathtt{0}}}^{{\mathtt{1}}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{x}}\right)}\right)}{d{\mathtt{x}}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{1}}^\circ\right)}$$

and 

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{1}}^\circ\right)} = {\mathtt{0.017\: \!452\: \!406\: \!437}}$$

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Thanks Alan