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A locally rotationally symmetric Bianchi-I model filled with strange quark matter is explored in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mn>2</mn><mi>f</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity, where <i>R</i> is the Ricci scalar, <i>T</i> is the trace of the energy-momentum tensor and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> is an arbitrary constant. Exact solutions are obtained by assuming that the expansion scalar is proportional to the shear scalar. The model is found to be physically viable for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo><</mo><mo>−</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></semantics></math></inline-formula>. Strange quark matter at early times mimics ultra-relativistic radiation whereas at late times it behaves as dust, quintessence, or even the cosmological constant for some specified values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>. The effective matter acts as stiff matter irrespective of the matter content and of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity. The model is shear-free at late times but remains anisotropic throughout the evolution.