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Figure 7-36 shows that this should work when there is no load. As shown in figures 7-12/13, output voltages 1 V from the rails should work with 20 mA output current.
What is the exact voltage at which this happens? What is the load?
Some of my comments here will reinforce what Clemens and Alex said.
When you see distortion as the signal amplitude is increases, this is generally from slew-rate limitations. There is a theoretical relationship VmaxPeak = SR/(2*pi*f), that shows the maximum signal amplitude without slew-induced distortion. This relationship is generally a good indication of visible distortion (distortion that is obvious on the oscilloscope). However, as you approach the limit you will get increased distortion that may not be obvious, and when you surpass the limit the distortion should be obvious. Note: VmaxPeaktoPeak = 2VmaxPeak (i.e. sometimes it is specified as peak-to-peak).
The equation doesn't take into account the small-signal versus large-signal transition point. The equation also, does not consider the effects of slew boost. This can introduce some inaccuracy in the curve (Figure 7-36 in this case).
I recently have had a few questions on the the OPA2182 and OPA2189 regarding the full-power bandwidth curve. I am still working on fully resolving the discrepancies that we have found. For most op amp data sheets the full-power bandwidth curve is calculated using the equation: VmaxPeak = SR/(2*pi*f). For the OPA2182 the full-power-bandwidth curve is slightly different than what is indicated by VmaxPeak = SR/(2*pi*f) (off by a factor of 2). The published curve is more conservative than the equation and may be a measured curve. In any case, I measured the circuit in a buffer configuration at 200kHz and the data sheet curve did a better job of predicting distorted signal than the equation.
Ultimately, the full-power bandwidth curves are a guideline and staying inside the "safe" limit does not mean zero distortion. Keep in mind that the curve is a typical curve and may not include effects like slew-boost and also the small signal to large signal transition point. I think a good practice is to make sure that your signal frequency / amplitude should be a decade from the boundary of the graph.
Below is my measured results and a comparison of the ideal curve to the published curve. I think your signal is at 4Vpk (8Vpp) and 100kHz. If you check figure 7-36 you will see that you are inside the "safe" region but close to the curve. I think you just need a device with higher slew-rate(OPA189 or OPA2888). Note that measured results for OPA189 are also in the attachment below. This device curve also doesn't match the expected equation but in this case I think it is a data-sheet error as the theoretical curve compares well to measurements.
Thus, at this frequency you should not expect slew induced distortion. Any distortion you see is due to loading effects or some other issue. You should disconnect the amplifier output to see if the distortion goes away.
